Search results for "Fourier Transforms" - Rhea

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• Discrete Fourier Transform table
  Discrete Fourier transforms (DFT) Pairs and Properties ...colspan="2" | Discrete Fourier Transform Pairs and Properties [[Discrete Fourier Transform|(info)]]
  4 KB (633 words) - 15:28, 23 April 2013
• Snikitha ListECE301
  ...ansform. Discrete-time linear systems: difference equations, Discrete-Time Fourier Transform, bilateral z-Transform. Sampling, quantization, and discrete-time ...me Fourier transforms and an ability to compute the transforms and inverse transforms of basic examples using methods such as partial fraction expansions.
  3 KB (394 words) - 07:08, 4 May 2010
• My use for the DFT!
  [[Category:discrete Fourier transform]] ...reek letter has been added. So the goal should be to make such math (these transforms rather) and relate them to real life, not just by telling us where it used
  13 KB (2,348 words) - 13:25, 2 December 2011
• 2010 Fall ECE 438 Boutin
  ..._inverse_z-transforms_ECE438F10|questions about z-transforms and inverse-z-transforms]] ...ed exercises of Fourier series computations for CT signals]], especially [[Fourier series coefficients student 1|this one]].
  9 KB (1,221 words) - 11:00, 22 December 2014
• Lecture Schedule ECE438Fall10 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  9 KB (1,331 words) - 07:15, 29 December 2010
• Lecture2ECE438F10
  In the second lecture, we introduced the CT Fourier transform in terms of frequency "f" and discussed its relationship with the ...ent_summary_CT_DT_Fourier_transform_ECE438F09|Summary of CT and DT Fourier transforms]]
  1 KB (212 words) - 04:24, 27 October 2010
• Lecture5ECE438F10
  ...format as the one use for this [[Laplace_Transforms_Table|table of Laplace transforms]].)
  2 KB (233 words) - 07:52, 7 September 2010
• Sampling pure frequencies ECE438F10
  ...is the idea. But you should also note the similarities between the Fourier transforms (not just the differences). --[[User:Mboutin|Mboutin]] 12:07, 7 September 2
  1 KB (222 words) - 08:07, 7 September 2010
• Recommended exercise Fourier series computation
  [[Category:Fourier series continuous-time]] = This pages contains exercises to practice computing the Fourier series of a CT signal =
  5 KB (797 words) - 09:43, 29 December 2010
• Lecture8ECE438F10
  In Lecture #8, I showed by example how to compute inverse z-transforms. I gave students two exercises (case b) and case c) in your notes) to try a For those of you wishing to brush up on Fourier series, here are two collective study pages:
  875 B (123 words) - 12:42, 10 September 2010
• CT DT Fourier transform ECE438F10
  [[Category:Fourier transform]] == The Continuous Time Fourier Transform (CTFT) ==
  4 KB (746 words) - 08:47, 11 November 2013
• Table DT Fourier Transforms
  [[Category:Fourier transform]] [[Discrete-time_Fourier_transform_info|Discrete-time (DT) Fourier Transforms]] Pairs and Properties
  7 KB (1,037 words) - 21:05, 4 March 2015
• DTFT rectangular window
  =About the Fourier Tranform of a Rectangular Window in discrete-time= [[Table_DT_Fourier_Transforms|Back to the table of DT Fourier transforms]]
  382 B (52 words) - 12:59, 22 October 2010
• Lecture36ECE438F10
  ...understanding how to extent these to the 2D versions of the other Fourier transforms we say (e.g., DTFT and DFT). We also defined some basic 2D signals. [[Category:continuous-space Fourier transform]]
  977 B (131 words) - 09:30, 11 November 2011
• Info multiplication property FT w
  =About the Multiplication Property of the continuous-time Fourier transform= The multiplication property of the continuous-time Fourier transform can be stated as follows:
  751 B (105 words) - 16:17, 30 November 2010
• 2011 Spring ECE 301 Boutin
  *Video Extract of a talk by Prof. Joe Havlicek explaining the meaning of the Fourier transform very clearly using music. *Computing the Fourier series coefficients of a CT signal
  18 KB (2,485 words) - 10:36, 11 November 2011
• ECE301 signals systems formulas
  *[[CT Fourier Transform (frequency in radians per time unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</spa *[[Table DT Fourier Transforms|Discrete-time Fourier Transform Pairs and Properties]]
  890 B (101 words) - 17:30, 21 April 2013
• Signals and systems practice problems list
  *[[CT_Fourier_series_practice_problems_list|Problems on continuous-time Fourier series]] *[[CT_Fourier_transform_practice_problems_list|Problems on continuous-time Fourier transform]]
  12 KB (1,768 words) - 10:25, 22 January 2018
• Lecture17ECE301S11
  ...ible to compute; this was exemplified when we tried to compute the inverse Fourier transform of the constant function 1. *Solve the following practice problem on CT Fourier transform.
  1 KB (161 words) - 14:12, 28 February 2011
• HW7 ECE301 Spring2011 Prof Boutin
  ...en check your answer using this [[Table_DT_Fourier_Transforms| table of DT Fourier transform pairs and properties]]. (Explain how you checked your answer.) ...ransform (i.e., the integral formula) to compute the inverse Discrete-time Fourier transform of the signal
  4 KB (695 words) - 18:23, 7 March 2011
• ECE301inBME
  ...r_Transform_Video |Fourier]]/Laplace/[[Compute z-transform u n ECE301S11|Z transforms]] from [[2011 Spring ECE 301 Boutin|ECE301]]!) are utilized to convert, fil ...nications, and networking. Imaging techniques involving diffraction and/or Fourier analysis with application to tomography, magnetic resonance imaging, synthe
  17 KB (2,368 words) - 10:53, 6 May 2012
• Nyquist rate for a sinc function
  Yes, this signal is band limited. It is a sinc function, and its Fourier transform can be found using the table of formulas in the textbook on page ...in the correct max frequency of the signal. It would be ok to say that the Fourier transform is a non-zero constant multiple of a low-pass filter with gain 1
  3 KB (431 words) - 10:28, 11 November 2011
• HW9 ECE301 Spring2011 Prof Boutin Solutions
  ...says that <br> <math>\frac{2 \sin \left( W t \right)}{\pi t } \ </math> transforms to <math>\left\{\begin{array}{ll}1, & \text{ if }|\omega| <W,\\ 0, & \text ...he Fourier transform of the CT signal representing the sampling in CT. The Fourier transform of the DT signal obtained by storing the values of the samples in
  9 KB (1,462 words) - 07:01, 22 April 2011
• Nyquist rate after multiplicating sinc signals ECE301S11
  ...e product of two functions is (1/2pi) times the convolution of the Fourier transforms of the individual functions.
  2 KB (336 words) - 10:31, 11 November 2011
• Review of an alternative book by M.J. Roberts
  In this chapter author explains Fourier Series and Fourier Transforms of CT signals. The explanation is very good and clear. It is very similar t ...in more general form and it is very good because ECE students use Laplace Transforms everywhere and it is very easy to follow the chapter especially with the cl
  6 KB (972 words) - 06:29, 1 November 2011
• Book Review: Signals & Systems MJR
  In this chapter author explains Fourier Series and Fourier Transforms of CT signals. The explanation is very good and clear. It is very similar t ...in more general form and it is very good because ECE students use Laplace Transforms everywhere and it is very easy to follow the chapter especially with the cl
  6 KB (955 words) - 10:54, 6 May 2012
• Lecture Schedule ECE438Fall11 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  9 KB (1,341 words) - 03:52, 31 August 2013
• Lecture2ECE438F11
  ...in the [[Lecture3ECE438F11|next lecture]], we shall compute their Fourier transforms. **[[practice_CTFT_computation_rect_and_sinc_ECE438F11|Compute the Fourier transform of a rect and a sinc]]
  2 KB (285 words) - 12:48, 21 September 2011
• Lecture3ECE438F11
  ...he definition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. **[[Practice DTFT computation cosine ECE438F11|What is the Fourier transform of this DT cosine?]]
  2 KB (252 words) - 12:48, 21 September 2011
• Practice DTFT computation rect ECE438F11
  [[Category:discrete time Fourier transform]] Topic: Discrete-time Fourier transform computation
  6 KB (1,090 words) - 12:35, 26 November 2013
• Compute DSFT cosine ECE438F11
  [[Category:discrete-space Fourier transform]] Topic: Discrete-space Fourier transform computation
  4 KB (703 words) - 12:59, 26 November 2013
• ECE538
  *[[CT_Fourier_Transform_(frequency_in_radians_per_time_unit)|Continuous-time Fourier Transform Pairs and Properties]] *[[Table_DT_Fourier_Transforms|Discrete-time Fourier Transform Pairs and Properties]]
  1 KB (152 words) - 12:17, 24 February 2015
• Upsham Dawra - Professional Statement
  ...ure and Compilers, along with classes like Signals and Systems and Fourier Transforms. This afforded me a venerable arsenal of knowledge in both Electrical and C
  3 KB (550 words) - 12:22, 9 February 2012
• Professional statement DerekRichards ECE400S12
  ...n signal analysis classes, which don’t just teach how to compute Fourier transforms, and what to do with that answer. They teach the idea that any signal can b
  4 KB (666 words) - 12:13, 9 February 2012
• Lecture4ECE438F13
  ...he definition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. *[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]]
  3 KB (398 words) - 06:10, 3 September 2014
• 2018 Fall ECE 301 Boutin
  | [[FourierSeriesConvergenceBonusProject | Convergence of Parametric Fourier Series]] | [[The_2-D_Fourier_Transform_and_Images|The 2-D Fourier Transform and Images]]
  4 KB (534 words) - 19:10, 4 December 2018
• 2012 ECE 301 Dr. Love
  *[[CT Fourier Transform (frequency in radians per time unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</spa *[[Table DT Fourier Transforms|Discrete-time Fourier Transform Pairs and Properties]]
  2 KB (236 words) - 11:24, 21 September 2012
• Lab 2 Additional Information ECE637 Spring2013 Bouman
  ...tifacts, people apply different type of windows before applying orthogonal transforms. ;'''Q - Section 2 - For calculationg Sx anlyitically, is this just doing a Fourier transform of and multiplying by its complex conjugate and 1/(N^2)? Not exa
  5 KB (957 words) - 08:11, 9 April 2013
• ECE637 Bouman lectures Image Processing sLecture mhossain
  ** [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]] ...te_parameter_signals_and_systems_discrete_transforms_S13_mhossain|Discrete Transforms]]
  2 KB (246 words) - 07:21, 26 February 2014
• ECE301 signals systems lecture notes
  ...ure19 ECE301Fall2008mboutin|Lecture 19]]: TA Example Session w/ DT Fourier Transforms and inverses
  3 KB (328 words) - 17:57, 30 November 2018
• Lecture42 blog ECE302S13 Boutin
  ...USE A [[CT_Fourier_Transform_%28frequency_in_hertz%29|TABLE OF CT FOURIER TRANSFORMS]] TO DO THESE PROBLEMS.
  4 KB (545 words) - 07:12, 24 April 2013
• Lecture43 blog ECE302S13 Boutin
  ...USE A [[CT_Fourier_Transform_%28frequency_in_hertz%29|TABLE OF CT FOURIER TRANSFORMS]] TO DO THESE PROBLEMS.
  3 KB (434 words) - 07:02, 24 April 2013
• ECE637 tomographic reconstruction intro S13 mhossain
  ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]] ...as [[ECE637_tomographic_reconstruction_radon_transform_S13_mhossain|Radon Transforms]]. Projections must be collected at every angle <math>\theta</math> and dis
  8 KB (1,168 words) - 07:24, 26 February 2014
• Linear algebra tutorials
  *[[ECE662_Whitening_and_Coloring_Transforms_S14_MH|Whitening and coloring transforms]] ...n_of_the_Divide_and_Conquer_DFT_via_Matrices|"divide and conquer" Discrete Fourier Transform (DFT)]]
  2 KB (293 words) - 12:25, 27 March 2015
• Lemma boutin mhossain 05 2013
  * the Fourier transforms of their pdfs exist Taking the inverse Fourier transform, we get<br/>
  6 KB (1,084 words) - 13:20, 13 June 2013
• ECE637 discrete parameter signals and systems discrete transforms S13 mhossain
  ...te_parameter_signals_and_systems_discrete_transforms_S13_mhossain|Discrete Transforms]] <font size= 3> Subtopic 1: Discrete Transforms </font size>
  10 KB (1,726 words) - 07:26, 26 February 2014
• Lecture Schedule ECE438Fall13 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  9 KB (1,353 words) - 09:04, 11 November 2013
• Lecture7ECE438F13
  ...sform. As we will see later, this trick will be very handy for inverting z-transforms in general. **[[practice_DTFT_computation_sine_ECE438F13|Compute the DT Fourier transform of a sinc]]
  3 KB (386 words) - 06:09, 11 September 2013
• HW1 Solution ECE438F13
  [[Category:fourier transform]] ...ier_Transform_%28frequency_in_radians_per_time_unit%29|table of CT Fourier transforms]] in terms of <math>\omega</math> in radians and to obtain the correspondin
  5 KB (768 words) - 05:49, 9 September 2013
• HWK8MA527Fall2013
  From here I solved for Bn. The fourier series I calculated is F(x) = 2/pi sinx - 2/4pi sin2x + 2/9pi sin3x ... Whe and by differentiation of transforms, L{tf(t)} = - derivative( (1+k)/(s^2 + (1+k)^2) )&nbsp;?
  7 KB (1,302 words) - 04:58, 23 October 2013
• ECE438 digital signal processing textbooks
  ...man/ece438/lecture/module_1/1.5_z_transform/1.5.4_zt_and_ccf_diff_eq.pdf Z-transforms and differerence equations] ...ue.edu/~bouman/ece438/lecture/module_1/1.3_fourier_analysis/1.3.3_dtft.pdf Fourier analysis]
  6 KB (759 words) - 08:10, 11 November 2013
• ECE438 digital signal processing formulas
  *[[Laplace Transforms Table|Laplace Transform Pairs and Properties]] *[[CT Fourier Transform (frequency in hertz)|Continuous-time Fourier Transform Pairs and Properties]]
  1,002 B (119 words) - 05:58, 28 October 2013
• ECE438 digital signal processing learning material
  *[[CT_DT_Fourier_transform_ECE438F10|Summary of CT and DT Fourier transform]] *[[Discrete_Fourier_transform_ECE438F10|Discrete Fourier transform]]
  4 KB (471 words) - 19:34, 9 February 2015
• HWK10MA527Fall2013
  ...ecognize that this integral is an instance of formulas (4) and (5) for the Fourier Integral formulas. Your problem is to figure out what the f(x) is. Table 1 in 11.10 on Page 534 is a table of Fourier Cosine Transforms.
  6 KB (1,130 words) - 18:15, 5 November 2013
• Review2MA527Fall2013
  from the point of view of Laplace transforms > For #4-b we are asked to find the real Fourier
  11 KB (1,959 words) - 17:57, 10 November 2013
• 2014 Fall ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  13 KB (1,944 words) - 16:51, 13 March 2015
• Lecture Schedule ECE438Fall14 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  9 KB (1,320 words) - 04:46, 11 September 2014
• Lecture4ECE438F14
  ...he definition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. *[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]]
  2 KB (339 words) - 05:39, 8 September 2014
• Slecture Fourier transform w f ECE438 review
  ...ransform w f ECE438|Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f]] </font> I liked that you compared the formulas for the Fourier Transforms in both the w and f forms. Showing a few more steps in the second example w
  5 KB (843 words) - 05:30, 15 October 2014
• Ftrepcomb mattmiller
  Fourier Transform of Rep and Comb Functions In this slecture, we are going to look at the fourier transforms of the <math>comb_T()</math> and <math>rep_T()</math> functions.
  4 KB (734 words) - 18:56, 16 March 2015
• Lecture24ECE438F14
  Today we discussed the computation of z-transforms and inverse z-transforms. ...ce_z_transform_computation_3_ECE438F13|Compute this z-transform and obtain Fourier transform]]
  4 KB (446 words) - 05:56, 22 October 2014
• Lecture Schedule ECE438Fall15 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  10 KB (1,356 words) - 13:19, 19 October 2015
• 2015 Summer ECE 301 Jang
  ...tter size both-sided crib sheet is allowed. Closed-book and no calculator. Fourier Transform Tables (both CTFT and DTFT) will be given. Chap 3. Fourier Series for Periodic Signals
  6 KB (748 words) - 21:35, 10 August 2015
• 2015 Fall ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  6 KB (845 words) - 15:37, 4 November 2016
• Lecture4ECE438F15
  ...he definition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. *[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]]
  3 KB (382 words) - 16:41, 31 August 2015
• 2015 Fall ECE 438 Boutin A visual explanation of aliasing and repetition with the DTFT Erik Swan
  ...is the Discrete Time Fourier Transform (DTFT). Unlike the Continuous Time Fourier Transform (CTFT), the DTFT of a signal is periodic with period <math>2\pi</ ...we'll assume the reader has a good intuitive understanding of the CTFT and Fourier series, and is generally familiar with the DTFT.
  12 KB (2,004 words) - 20:37, 2 December 2015
• 2016 Fall ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  4 KB (622 words) - 09:42, 8 January 2017
• Lecture Schedule ECE438Fall16 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  10 KB (1,357 words) - 17:02, 14 September 2016
• Lecture Schedule ECE438Spring17 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  10 KB (1,357 words) - 09:45, 8 January 2017
• 2017 Fall ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  3 KB (421 words) - 16:18, 10 December 2017
• 2017 Spring ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  3 KB (448 words) - 23:55, 23 April 2017
• X-Ray Crystallography
  A Brief Overview of X-Ray Crystallography and how Spatial Fourier Transforms are Applicable in the Method.
  351 B (57 words) - 16:24, 23 April 2017
• The Laurent Series in DSP
  ...'z''') as well. The Laurent Series is the link in DSP between the Discrete Fourier Transform ('''DFT''') and the Z-Transform. ...anding of the Laurent Series can then help with computing more difficult Z-transforms, either forward or backward. The concepts involved in finding a Laurent Ser
  6 KB (931 words) - 23:40, 23 April 2017
• MathSquadPages
  *[[Fourier_analysis_in_Music| Fourier Analysis in Music]] by [[user:mbell|Maria Bell]] **[[Laplace Transforms]]
  3 KB (370 words) - 09:55, 12 January 2018
• ECE301Spring18-DeterminingSignalPropertiesThroughFourierExam
  == ''Determining the Properties of a Signal Based on its Fourier Transform'' == As part of this course, it is important to be able to examine the Fourier Transform of a signal, and tell if the original signal is real, pure imagin
  6 KB (1,010 words) - 18:04, 20 April 2018
• 2018 Fall ECE 301 Boutin Fourier Transforms in MP3 Audio Compression Shubham Bhokare comments
  ...Boutin_Fourier Transforms in MP3 Audio Compression_Shubham Bhokare|Fourier Transforms in MP3 Audio Compression]] ...Boutin_Fourier Transforms in MP3 Audio Compression_Shubham Bhokare|Fourier Transforms in MP3 Audio Compression]]. Please leave me a comment below if you have any
  990 B (139 words) - 11:04, 28 November 2018
• 2018 Fall ECE 301 Boutin Fourier Transforms in MP3 Audio Compression Shubham Bhokare
  <center><font size= 4>Fourier Transforms in MP3 Audio Compression</font size> ==[[2018_Fall_ECE _301_Boutin_Fourier Transforms in MP3 Audio Compression_Shubham Bhokare_comments | Questions and comments]
  2 KB (216 words) - 11:04, 28 November 2018
• Moving between the Time Domain and Frequency Domain
  ...w \phantom{aaa} \downarrow \phantom{aaa} \downarrow \phantom{aaa} \textrm{Fourier transform} </math> ...ely, can be multiplied together to obtain Y(ω), and Y(ω) can be inverse Fourier transformed to find y(t). Though this process requires more steps, its comp
  5 KB (865 words) - 16:23, 2 December 2018
• Use of Fourier Transforms in MP3 Audio Compression
  =Use of Fourier Transforms in MP3 Audio Compression= With MP3, the sound samples are transformed using methods that involve Fourier Series Transformations. A frequency analysis of the sound is the basis for
  5 KB (752 words) - 17:40, 2 December 2018
• Filtering Sound with Adobe Audition
  ...d welcome to a tutorial on filtering and understanding sound using Fourier Transforms! While this tutorial will use Adobe Audition(TM), everything shown below ca ...rcises in '''ECE 301''', this tutorial will let you analyze visual Fourier Transforms, intelligently apply frequency filters, and gain a better understanding of
  6 KB (1,077 words) - 20:29, 7 April 2019
• ECE 301 self-analysis of exam performance
  ...olutions is important. For example, in the case of Continuous time Fourier transforms of periodic signals, the answer is speculated then proven to be the correct
  3 KB (583 words) - 21:07, 24 April 2019
• Practice Exam solutions with reflection ECE301S19
  ...olutions is important. For example, in the case of Continuous time Fourier transforms of periodic signals, the answer is speculated then proven to be the correct
  4 KB (644 words) - 11:22, 30 April 2019
• 2019 Fall ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  4 KB (467 words) - 02:18, 10 December 2019
• Lecture Schedule ECE438Fall2019 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  10 KB (1,356 words) - 18:52, 20 August 2019
• 2020 Fall MA 271 Walther
  | [[Walther_MA271_Fall2020_topic20|Fourier transforms]]
  6 KB (846 words) - 17:57, 7 December 2020
• Walther MA271 Fall2020 topic20
  = Fourier Transforms = ...representing how much of each frequency is prevalent in the function. The Fourier transform allows for signals to be broken into their individual frequency c
  12 KB (2,051 words) - 14:20, 5 December 2020
• Definition of Nyquist’s Theorem
  ...[https://en.wikipedia.org/wiki/Fourier_transform here]. As a result of the Fourier Transform, the graph of a waveform can be converted into one similar to the ...e not equivalent at frequencies close to ''B'', have Discrete Time Fourier Transforms that are the same. This situation results because there is an overlap betwe
  4 KB (707 words) - 23:06, 6 December 2020