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− | [ | + | [https://www.projectrhea.org/learning/practice.php Practice Problems] on Signals and Systems |
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− | ==Subtopics== | + | <div style="font-family: Verdana, sans-serif; font-size: 14px; text-align: justify; width: 70%; margin: auto; border: 1px solid #aaa; padding: 2em;"> |
+ | ==Related Subtopics == | ||
*[[CT_Fourier_series_practice_problems_list|Problems on continuous-time Fourier series]] | *[[CT_Fourier_series_practice_problems_list|Problems on continuous-time Fourier series]] | ||
*[[CT_Fourier_transform_practice_problems_list|Problems on continuous-time Fourier transform]] | *[[CT_Fourier_transform_practice_problems_list|Problems on continuous-time Fourier transform]] | ||
+ | </div> | ||
---- | ---- | ||
==Collectively solved problems related to Signals and Systems== | ==Collectively solved problems related to Signals and Systems== | ||
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**[[Magnitude complex CT signals ECE301S11|Compute the magnitude of these two CT signals]] | **[[Magnitude complex CT signals ECE301S11|Compute the magnitude of these two CT signals]] | ||
**[[Magnitude complex DT signals ECE301S11|Compute the magnitude of these three DT signals]] | **[[Magnitude complex DT signals ECE301S11|Compute the magnitude of these three DT signals]] | ||
− | *Signal Power and Energy | + | *Signal [[Signal_power_CT|Power]] and [[Signal_energy_CT|Energy]] in CT |
− | **[[Signal power energy exercise CT ECE301S11|Compute the power and energy of the following | + | **[[Signal power energy exercise CT ECE301S18 exponential|Compute the power and energy of a (CT) exponential]] |
+ | **[[Signal power energy exercise CT ECE301S18 sin|Compute the power and energy of a (CT) sine]] | ||
+ | **[[Signal power energy exercise CT ECE301S11|Compute the power and energy of a complex (CT) exponential]] | ||
+ | **[[HW1.5_Brian_Thomas_-_Energy_and_Power_of_a_Complex_Signal_over_Infinite_Time_ECE301Fall2008mboutin|Energy of x(t)= cos(t)+j sin(t)]] | ||
+ | **[[Calculating_E_infinity_and_P_infinity_-_Jonathan_Chu_(Chu7)|Compute the power and energy of t times a step function]] | ||
+ | **[[Calculating_E_infinity_and_P_infinity_-_Stuart_Pulliam_(spulliam)|Compute the power and energy of 2 times t squared]] | ||
+ | **[[Vishal_Ramani_vramani|Compute the power and energy of a square root]] | ||
+ | **[[Calculating_E_infinity_and_P_infinity_-_Tylor_Thompson_(thompso7)|Compute the power and energy of a square root times a step function]] | ||
+ | **[[E_infinity_and_P_infinity_-_Evan_Witkoske|Compute the power and energy of 5 j times sin(t)]] | ||
+ | **[[P_infinity_2j|Compute the power of 2j ]] | ||
+ | *Signal Power and Energy in DT | ||
+ | **[[Signal power energy exercise DT ECE301S18|Compute the power and energy of the following DT exponential signal]] | ||
**[[Signal power energy exercise DT ECE301S11|Compute the power and energy of the following DT signal]] | **[[Signal power energy exercise DT ECE301S11|Compute the power and energy of the following DT signal]] | ||
*Transformation of the independent variable | *Transformation of the independent variable | ||
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**[[Fourier_series_coefficients_pulse_train_CT_ECE301S11|Obtain the Fourier series coefficients of this DT pulse-train]] | **[[Fourier_series_coefficients_pulse_train_CT_ECE301S11|Obtain the Fourier series coefficients of this DT pulse-train]] | ||
**[[Recommended_exercise_Fourier_series_computation_DT|A page containing several practice problems on computing Fourier series of a CT signal]] | **[[Recommended_exercise_Fourier_series_computation_DT|A page containing several practice problems on computing Fourier series of a CT signal]] | ||
− | * | + | *Fourier transform of a continuous-time signal: |
− | **[[ | + | **See [[CT_Fourier_transform_practice_problems_list|subtopic page]] for a list of all problems on Fourier transform of a CT signal |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
*Computing the Fourier transform of a discrete-time signal: | *Computing the Fourier transform of a discrete-time signal: | ||
**[[Fourier_transform_3numinusn_DT_ECE301S11|Compute the Fourier transform of 3^n u[-n]]] | **[[Fourier_transform_3numinusn_DT_ECE301S11|Compute the Fourier transform of 3^n u[-n]]] | ||
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**[[Signal modulation with cosine ECE301S11|Demodulation of signal modulated with cosine]] | **[[Signal modulation with cosine ECE301S11|Demodulation of signal modulated with cosine]] | ||
*Z-transform | *Z-transform | ||
+ | **[[Practice_prove_modulation_property_z_transform|Prove the modulation property of the z-transform]] | ||
**[[Compute z-transform u n ECE301S11|Computation of the z-transform]] | **[[Compute z-transform u n ECE301S11|Computation of the z-transform]] | ||
**[[Compute z-transform u -n ECE301S11|Another computation of the z-transform]] | **[[Compute z-transform u -n ECE301S11|Another computation of the z-transform]] | ||
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**[[practice_z_transform_computation_1_ECE438F13|Compute this z-transform]] | **[[practice_z_transform_computation_1_ECE438F13|Compute this z-transform]] | ||
**[[practice_z_transform_computation_2_ECE438F13|Compute this z-transform]] | **[[practice_z_transform_computation_2_ECE438F13|Compute this z-transform]] | ||
− | + | **[[practice_z_transform_computation_3_ECE438F13|Compute this z-transform and obtain Fourier transform]] | |
+ | **[[Practice_Question_inverse_z_transform_1_ECE438F13|Obtain the inverse z-transform]] | ||
+ | **[[Practice_Question_inverse_z_transform_2_ECE438F13|Obtain the inverse z-transform]] | ||
+ | **[[Practice_Question_inverse_z_transform_3_ECE438F13|Obtain the inverse z-transform]] | ||
+ | **[[Practice_Question_inverse_z_transform_4_ECE438F13|Obtain the inverse z-transform]] | ||
+ | **[[Practice_Question_inverse_z_transform_5_ECE438F13|Obtain the inverse z-transform]] | ||
+ | **[[Practice_Question_inverse_z_transform_6_ECE438F13|Obtain the inverse z-transform]] | ||
+ | **[[Practice_Question_inverse_z_transform_example_S15|Obtain the inverse z-transform]] | ||
---- | ---- | ||
=Problems from the official textbook (Oppenheim WIllsky)= | =Problems from the official textbook (Oppenheim WIllsky)= | ||
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*[[4.5_ECE301Fall2008mboutin]] | *[[4.5_ECE301Fall2008mboutin]] | ||
*[[ECE_301_Fall_2007_mboutin_Homework_5|Discussion about problem 5.31]] | *[[ECE_301_Fall_2007_mboutin_Homework_5|Discussion about problem 5.31]] | ||
+ | ---- | ||
+ | ==Quizzes with solution== | ||
+ | *From instructor Jang, Summer 2015 | ||
+ | **[[Media:301Quiz1.pdf|Quiz 1. Linear and Time Invariant]] (pdf) | ||
+ | **[[Media:301Quiz2.pdf|Quiz 2. Convolution of Two Rectangles]] (pdf) | ||
+ | **[[Media:301Quiz3.pdf|Quiz 3. Continuous-Time Fourier Transform Exercise]] (pdf) | ||
+ | **[[Media:301Quiz4.pdf|Quiz 4. Continuous-Time Fourier Transform Equation]] (pdf) | ||
+ | **[[Media:301Quiz5.pdf|Quiz 5. Nyquist Sampling Theorem]] (pdf) | ||
+ | **[[Media:301Quiz6.pdf|Quiz 6. Discrete-Time Fourier Transform Exercise]] (pdf) | ||
+ | **[[Media:301Quiz7.pdf|Quiz 7. Sampling Theory]] (pdf) | ||
---- | ---- | ||
==More Practice Problems== | ==More Practice Problems== | ||
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*[[ECE_301_Fall_2007_mboutin_Convolution|Example of CT convolution]] | *[[ECE_301_Fall_2007_mboutin_Convolution|Example of CT convolution]] | ||
*[[Exercise_1_ECE301Fall2008mboutin|Is this system time-invariant?]] | *[[Exercise_1_ECE301Fall2008mboutin|Is this system time-invariant?]] | ||
+ | *[[InverseZtransform|Inverse z-transform: summary of theory and practice examples with solutions]] | ||
*[[Examples_ECE301Fall2008mboutin|practice problems (mostly on Fourier transform)]] | *[[Examples_ECE301Fall2008mboutin|practice problems (mostly on Fourier transform)]] | ||
*[[ECE301_S11_Exam_3_more_practice|Finale exam practice (written by a student)]] | *[[ECE301_S11_Exam_3_more_practice|Finale exam practice (written by a student)]] | ||
---- | ---- | ||
[[ECE301|Back to ECE301: "Signals and Systems"]] | [[ECE301|Back to ECE301: "Signals and Systems"]] |
Latest revision as of 10:25, 22 January 2018
Practice Problems on Signals and Systems
(ECE301)
Contents
Related Subtopics
- Review of complex numbers
- Signal Power and Energy in CT
- Compute the power and energy of a (CT) exponential
- Compute the power and energy of a (CT) sine
- Compute the power and energy of a complex (CT) exponential
- Energy of x(t)= cos(t)+j sin(t)
- Compute the power and energy of t times a step function
- Compute the power and energy of 2 times t squared
- Compute the power and energy of a square root
- Compute the power and energy of a square root times a step function
- Compute the power and energy of 5 j times sin(t)
- Compute the power of 2j
- Signal Power and Energy in DT
- Transformation of the independent variable
- Basic System Properties
- Is the following system invertible?
- Is the following system invertible? New! Waiting for input!
- Is the following system invertible? New! Waiting for input!
- Is the following system invertible? New! Waiting for input!
- Is the following system invertible? New! Waiting for input!
- Is the following system invertible? New! Waiting for input!
- Is the following system stable?
- Is the following system memoryless?
- Is the following system causal?
- Linearity and time invariance of a system
- Linearity and time invariance
- Computing the output of a DT LTI system by convolution
- Compute the output of the following DT LTI system
- Compute the output of the following DT LTI system
- Compute the output of the following DT LTI system
- Compute the output of the following DT LTI system
- Compute the output of the following DT LTI system
- Compute the output of the following DT LTI system
- Compute the output of the following DT LTI system
- Compute the output of the following DT LTI system
- Computing the output of a CT LTI system by convolution
- Computing the Fourier series coefficients of a CT signal
- See subtopic page for a list of all problems on Fourier series of a CT signal
- Computing the Fourier series coefficients of a DT signal
- Fourier transform of a continuous-time signal:
- See subtopic page for a list of all problems on Fourier transform of a CT signal
- Computing the Fourier transform of a discrete-time signal:
- Causal LTI systems defined by linear, constant coefficients difference equations:
- Nyquist theorem
- What is the Nyquist rate for this signal?
- What is the Nyquist rate for this other signal?
- Samping and reconstruction of sinc function.
- Samping and reconstruction of sinc function multiplied by exponential.
- Samping and reconstruction of sinc function multiplied by exponential (another one).
- Samping and reconstruction of sinc function multiplied by exponential (another one).
- Samping and reconstruction of sinc function multiplied by acosine.
- What is the Nyquist rate of a sinc function multiplied by itself?
- What is the Nyquist rate of the multiplication of two sinc functions?
- Modulation
- Z-transform
- Prove the modulation property of the z-transform
- Computation of the z-transform
- Another computation of the z-transform
- Computation of the inverse z-transform
- Another computation of the inverse z-transform
- Prove the scaling property of the z-transform
- compute the z-transform of this function
- Practice Question on z-transform computation
- Practice Question on inverse z-transform computation
- Compute this z-transform
- Compute this z-transform
- Compute this z-transform and obtain Fourier transform
- Obtain the inverse z-transform
- Obtain the inverse z-transform
- Obtain the inverse z-transform
- Obtain the inverse z-transform
- Obtain the inverse z-transform
- Obtain the inverse z-transform
- Obtain the inverse z-transform
Problems from the official textbook (Oppenheim WIllsky)
- 4.1_ECE301Fall2008mboutin
- 4.2_ECE301Fall2008mboutin
- 4.3_ECE301Fall2008mboutin
- 4.4_ECE301Fall2008mboutin
- 4.5_ECE301Fall2008mboutin
- Discussion about problem 5.31
Quizzes with solution
- From instructor Jang, Summer 2015
- Quiz 1. Linear and Time Invariant (pdf)
- Quiz 2. Convolution of Two Rectangles (pdf)
- Quiz 3. Continuous-Time Fourier Transform Exercise (pdf)
- Quiz 4. Continuous-Time Fourier Transform Equation (pdf)
- Quiz 5. Nyquist Sampling Theorem (pdf)
- Quiz 6. Discrete-Time Fourier Transform Exercise (pdf)
- Quiz 7. Sampling Theory (pdf)
More Practice Problems
- On Fourier transform
- Computing the energy and power of a CT signal: two examples
- Laplace transform example
- Frequency and impulse response from diff. eq.
- Example of CT convolution
- Is this system time-invariant?
- Inverse z-transform: summary of theory and practice examples with solutions
- practice problems (mostly on Fourier transform)
- Finale exam practice (written by a student)