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+ | [[Category:ECE301]] | ||
+ | [[Category:signals and systems]] | ||
[[Category:Problem_solving]] | [[Category:Problem_solving]] | ||
− | = | + | |
− | + | <center> | |
+ | <font size= 4> | ||
+ | [https://www.projectrhea.org/learning/practice.php Practice Problems] on Signals and Systems | ||
+ | </font size> | ||
+ | |||
+ | ([[ECE301]]) | ||
+ | </center> | ||
+ | ---- | ||
+ | <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_transform_practice_problems_list|Problems on continuous-time Fourier transform]] | ||
+ | </div> | ||
+ | ---- | ||
+ | ==Collectively solved problems related to Signals and Systems== | ||
*Review of complex numbers | *Review of complex numbers | ||
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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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*Basic System Properties | *Basic System Properties | ||
**[[Invertibility_of_a_system_ECE301S11|Is the following system invertible?]] | **[[Invertibility_of_a_system_ECE301S11|Is the following system invertible?]] | ||
+ | **[[Invertibility_of_a_system_question_1|Is the following system invertible?]]<span style="color:red"> New! Waiting for input! </span> | ||
+ | **[[Invertibility_of_a_system_question_2|Is the following system invertible?]] <span style="color:red"> New! Waiting for input! </span> | ||
+ | **[[Invertibility_of_a_system_question_3|Is the following system invertible?]] <span style="color:red"> New! Waiting for input! </span> | ||
+ | **[[Invertibility_of_a_system_question_4|Is the following system invertible?]] <span style="color:red"> New! Waiting for input! </span> | ||
+ | **[[Invertibility_of_a_system_question_5|Is the following system invertible?]] <span style="color:red"> New! Waiting for input! </span> | ||
**[[Stability_of_a_system_ECE301S11|Is the following system stable?]] | **[[Stability_of_a_system_ECE301S11|Is the following system stable?]] | ||
+ | **[[Memoryless system question ECE301S11|Is the following system memoryless?]] | ||
+ | **[[Causal system question ECE301S11|Is the following system causal?]] | ||
*Linearity and time invariance of a system | *Linearity and time invariance of a system | ||
**[[Time_invariance_of_a_system_ECE301S11|Is the following system time-invariant?]] | **[[Time_invariance_of_a_system_ECE301S11|Is the following system time-invariant?]] | ||
**[[Linearity_of_a_system_ECE301S11|Is the following system linear?]] | **[[Linearity_of_a_system_ECE301S11|Is the following system linear?]] | ||
− | *[[ | + | *Linearity and time invariance |
+ | **[[Time invariance of a system ECE301S11|Is the following system time-invariant?]] | ||
+ | **[[Linearity of a system ECE301S11|Is the following system linear?]] | ||
+ | **[[Answer from a previous student Time invariance of a system please comment ECE301S11|Is the following system time-invariant?]] | ||
*Computing the output of a DT LTI system by convolution | *Computing the output of a DT LTI system by convolution | ||
**[[output_of_LTI_DT_system_by_convolution_ECE301S11|Compute the output of the following DT LTI system]] | **[[output_of_LTI_DT_system_by_convolution_ECE301S11|Compute the output of the following DT LTI system]] | ||
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**[[output_of_LTI_CT_system_by_convolution_no4_ECE301S11|Compute the output of the following CT LTI system]] | **[[output_of_LTI_CT_system_by_convolution_no4_ECE301S11|Compute the output of the following CT LTI system]] | ||
*Computing the Fourier series coefficients of a CT signal | *Computing the Fourier series coefficients of a CT signal | ||
− | **[[ | + | **See [[CT_Fourier_series_practice_problems_list|subtopic page]] for a list of all problems on Fourier series of a CT signal |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
*Computing the Fourier series coefficients of a DT signal | *Computing the Fourier series coefficients of a DT signal | ||
**[[Fourier_series_coefficients_sinusoidal_DT_ECE301S11|Obtain the Fourier series coefficients of this DT sinusoidal]] | **[[Fourier_series_coefficients_sinusoidal_DT_ECE301S11|Obtain the Fourier series coefficients of this DT sinusoidal]] | ||
**[[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]]] | ||
**[[Fourier_transform_cosine_DT_ECE301S11|Compute the Fourier transform of cos(pi/6 n).]] | **[[Fourier_transform_cosine_DT_ECE301S11|Compute the Fourier transform of cos(pi/6 n).]] | ||
**[[Fourier_transform_window_DT_ECE301S11|Compute the Fourier transform of u[n+1]-u[n-2]]] | **[[Fourier_transform_window_DT_ECE301S11|Compute the Fourier transform of u[n+1]-u[n-2]]] | ||
− | + | **[[practice_DTFT_computation_sine_ECE438F13|Compute the DT Fourier transform of a sinc]] | |
+ | **[[practice_DTFT_computation_rect_ECE438F13|Compute the DT Fourier transform of a rect]] | ||
+ | *Causal LTI systems defined by linear, constant coefficients difference equations: | ||
+ | **[[Causal_LTI_System_Difference_Equation_no1_ECE301S11|Example of "typical" questions on causal LTI systems defined by difference equations]] | ||
+ | **[[ECE_301_Fall_2007_mboutin_Frequency_and_Impulse_Response_Example|Frequency and impulse response obtained from a difference equation describing an LTI system]] | ||
+ | **[[ECE_301_Fall_2007_mboutin_Difference_Equation_in_Class_Example|A tricky example: only attempt if you really understand what is going on]] | ||
+ | *Nyquist theorem | ||
+ | **[[Nyquist rate for a sinc function|What is the Nyquist rate for this signal?]] | ||
+ | **[[Nyquist rate for a signal ECE301S11|What is the Nyquist rate for this other signal?]]<span style="color: red"> | ||
+ | **[[Samping and reconstruction of sinc ECE301S11|Samping and reconstruction of sinc function]]. | ||
+ | **[[Samping and reconstruction of sinc multiplied by exponential ECE301S11|Samping and reconstruction of sinc function multiplied by exponential]]. | ||
+ | **[[Samping and reconstruction of sinc multiplied by exponential no1 ECE301S11|Samping and reconstruction of sinc function multiplied by exponential (another one)]]. | ||
+ | **[[Samping and reconstruction of sinc multiplied by exponential no2 ECE301S11|Samping and reconstruction of sinc function multiplied by exponential (another one)]]. | ||
+ | **[[Samping and reconstruction of sinc multiplied by cosine ECE301S11|Samping and reconstruction of sinc function multiplied by acosine]]. | ||
+ | **[[Nyquist rate after squaring sinc signals ECE301S11|What is the Nyquist rate of a sinc function multiplied by itself?]] | ||
+ | **[[Nyquist rate after multiplicating sinc signals ECE301S11|What is the Nyquist rate of the multiplication of two sinc functions?]] | ||
+ | *Modulation | ||
+ | **[[Signal modulation with exponential ECE301S11|Demodulation of signal modulated with exponential]] | ||
+ | **[[Signal modulation with cosine ECE301S11|Demodulation of signal modulated with cosine]] | ||
+ | *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|Another computation of the z-transform]] | ||
+ | **[[Compute Inverse z-transform ECE301S11|Computation of the inverse z-transform]] | ||
+ | **[[Compute Inverse z-transform 2 ECE301S11|Another computation of the inverse z-transform]] | ||
+ | **[[Practice prove z transform scaling property ECE438F11|Prove the scaling property of the z-transform]] | ||
+ | **[[Practice compute z transform windowed function|compute the z-transform of this function]] | ||
+ | **[[Practice_Question_2_ECE439F10|Practice Question on z-transform computation]] | ||
+ | **[[Practice_Question_3_ECE439F10|Practice Question on inverse z-transform computation]] | ||
+ | **[[practice_z_transform_computation_1_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)= | |
− | + | *[[4.1_ECE301Fall2008mboutin]] | |
− | [[ | + | *[[4.2_ECE301Fall2008mboutin]] |
+ | *[[4.3_ECE301Fall2008mboutin]] | ||
+ | *[[4.4_ECE301Fall2008mboutin]] | ||
+ | *[[4.5_ECE301Fall2008mboutin]] | ||
+ | *[[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== | ||
+ | *On Fourier transform | ||
+ | **[[Correct_CT_FT_1_ECE301Fall2008mboutin|Fourier transform problem]] | ||
+ | **[[Homework_10_ECE301Fall2008mboutin|A mistake NOT TO REPEAT when computing Fourier transforms]] | ||
+ | **[[Incorrect_CT_FT_periodic_signal_1_ECE301Fall2008mboutin|How NOT to take a Fourier transform]] | ||
+ | *[[E_infinity_and_P_infinity_calculations_-_William_Owens_%28wtowens%29|Computing the energy and power of a CT signal: two examples]] | ||
+ | *[[Ryan_Scott:_A_Laplace_example_from_class_ECE301Fall2008mboutin|Laplace transform example]] | ||
+ | *[[ECE_301_Fall_2007_mboutin_Frequency_and_Impulse_Response_Example|Frequency and impulse response from diff. eq.]] | ||
+ | *[[ECE_301_Fall_2007_mboutin_Convolution|Example of CT convolution]] | ||
+ | *[[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)]] | ||
+ | *[[ECE301_S11_Exam_3_more_practice|Finale exam practice (written by a student)]] | ||
+ | ---- | ||
+ | [[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)