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[[Category:ECE301]]
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[[Category:signals and systems]]
 
[[Category:Problem_solving]]  
 
[[Category:Problem_solving]]  
=[[:Category:Problem_solving|Practice Problems]] for Signals and Systems ([[ECE301]])=
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<center>
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<font size= 4>
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[https://www.projectrhea.org/learning/practice.php Practice Problems] on Signals and Systems  
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([[ECE301]])
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</center>
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----
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<div style="font-family: Verdana, sans-serif; font-size: 14px; text-align: justify; width: 70%; margin: auto; border: 1px solid #aaa; padding: 2em;">
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==Related Subtopics ==
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*[[CT_Fourier_series_practice_problems_list|Problems on continuous-time Fourier series]]
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*[[CT_Fourier_transform_practice_problems_list|Problems on continuous-time Fourier transform]]
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</div>
 
----
 
----
==Collectively solved [[:Category:Problem_solving|practice problems]] related to Signals and Systems==  
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==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  
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*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 CT signal]]  
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**[[Signal power energy exercise CT ECE301S18 exponential|Compute the power and energy of a (CT) exponential]]
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**[[Signal power energy exercise CT ECE301S18 sin|Compute the power and energy of a (CT) sine]]
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**[[Signal power energy exercise CT ECE301S11|Compute the power and energy of a complex (CT) exponential]]
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**[[HW1.5_Brian_Thomas_-_Energy_and_Power_of_a_Complex_Signal_over_Infinite_Time_ECE301Fall2008mboutin|Energy of x(t)= cos(t)+j sin(t)]]
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**[[Calculating_E_infinity_and_P_infinity_-_Jonathan_Chu_(Chu7)|Compute the power and energy of t times a step function]]
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**[[Calculating_E_infinity_and_P_infinity_-_Stuart_Pulliam_(spulliam)|Compute the power and energy of 2 times t squared]]
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**[[Vishal_Ramani_vramani|Compute the power and energy of a square root]]
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**[[Calculating_E_infinity_and_P_infinity_-_Tylor_Thompson_(thompso7)|Compute the power and energy of a square root times a step function]]
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**[[E_infinity_and_P_infinity_-_Evan_Witkoske|Compute the power and energy of 5 j times sin(t)]]
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**[[P_infinity_2j|Compute the power of 2j ]]
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*Signal Power and Energy in DT
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**[[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?]]
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**[[Invertibility_of_a_system_question_1|Is the following system  invertible?]]<span style="color:red"> New! Waiting for input! </span>
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**[[Invertibility_of_a_system_question_2|Is the following system  invertible?]] <span style="color:red"> New! Waiting for input! </span>
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**[[Invertibility_of_a_system_question_3|Is the following system  invertible?]] <span style="color:red"> New! Waiting for input! </span>
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**[[Invertibility_of_a_system_question_4|Is the following system  invertible?]] <span style="color:red"> New! Waiting for input! </span>
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**[[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?]]  
 
**[[Memoryless system question ECE301S11|Is the following system memoryless?]]  
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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
**[[Fourier_series_coefficients_sinusoidal_CT_ECE301S11|Obtain the Fourier series coefficients of this CT sinusoidal]]
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**See [[CT_Fourier_series_practice_problems_list|subtopic page]] for a list of all problems on Fourier series of a CT signal
**[[Fourier_series_coefficients_pulse_train_CT_ECE301S11|Obtain the Fourier series coefficients of this CT pulse-train]]
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**[[Fourier_series_coefficients_of_a_periodic_square_wave_period_two|Fourier series of a square wave]]
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**[[Fourier_series_coefficients_student_1|Fourier series of |sin(pi t)|]]
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**[[Recommended_exercise_Fourier_series_computation|A page containing several practice problems on computing Fourier series of a CT signal]]
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*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]]
*Computing the Fourier transform of a continuous-time signal:
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*Fourier transform of a continuous-time signal:
**[[Fourier_transform_etu_CT_ECE301S11|Compute the Fourier transform of e^-t u(t)]]
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**See [[CT_Fourier_transform_practice_problems_list|subtopic page]] for a list of all problems on Fourier transform of a CT signal
**[[Fourier_transform_cosine_CT_ECE301S11|Compute the Fourier transform of cos(2 pi t).]]
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**[[Fourier_transform_cosine_no2_CT_ECE301S11|Compute the Fourier transform of cos(2 pi t + pi/12).]]
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**[[Fourier_transform_periodic_rectangular_pulse_train_CT_ECE301S11|Compute the Fourier transform of a rectangular pulse-train]]
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**[[Fourier_transform_periodic_triangular_pulse_train_CT_ECE301S11|Compute the Fourier transform of a triangular pulse-train]]
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*Properties of the Fourier transform of a continuous-time signal:
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**[[Problem_on_time_shifting_and_time_scaling_property_of_Fourier_transform_ECE301S11Boutin|Derive a relationship between the FT of x(3t+7) and that of x(t)]]
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*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]]]
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**[[practice_DTFT_computation_sine_ECE438F13|Compute the DT Fourier transform of a sinc]]
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**[[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 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]]
 
**[[Causal_LTI_System_Difference_Equation_no1_ECE301S11|Example of "typical" questions on causal LTI systems defined by difference equations]]
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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  
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**[[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]]  
 
**[[Compute Inverse z-transform ECE301S11|Computation of the inverse 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]]
 
**[[Compute Inverse z-transform 2 ECE301S11|Another computation of the inverse z-transform]]
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**[[Practice prove z transform scaling property ECE438F11|Prove the scaling property of the z-transform]]
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**[[Practice compute z transform windowed function|compute the z-transform of this function]]
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**[[Practice_Question_2_ECE439F10|Practice Question on z-transform computation]]
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**[[Practice_Question_3_ECE439F10|Practice Question on inverse z-transform computation]]
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**[[practice_z_transform_computation_1_ECE438F13|Compute this z-transform]]
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**[[practice_z_transform_computation_2_ECE438F13|Compute this z-transform]]
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**[[practice_z_transform_computation_3_ECE438F13|Compute this z-transform and obtain Fourier transform]]
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**[[Practice_Question_inverse_z_transform_1_ECE438F13|Obtain the inverse z-transform]]
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**[[Practice_Question_inverse_z_transform_2_ECE438F13|Obtain the inverse z-transform]]
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**[[Practice_Question_inverse_z_transform_3_ECE438F13|Obtain the inverse z-transform]]
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**[[Practice_Question_inverse_z_transform_4_ECE438F13|Obtain the inverse z-transform]]
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**[[Practice_Question_inverse_z_transform_5_ECE438F13|Obtain the inverse z-transform]]
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**[[Practice_Question_inverse_z_transform_6_ECE438F13|Obtain the inverse z-transform]]
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**[[Practice_Question_inverse_z_transform_example_S15|Obtain the inverse z-transform]]
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----
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=Problems from the official textbook (Oppenheim WIllsky)=
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*[[4.1_ECE301Fall2008mboutin]]
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*[[4.2_ECE301Fall2008mboutin]]
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*[[4.3_ECE301Fall2008mboutin]]
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*[[4.4_ECE301Fall2008mboutin]]
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*[[4.5_ECE301Fall2008mboutin]]
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*[[ECE_301_Fall_2007_mboutin_Homework_5|Discussion about problem 5.31]]
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----
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==Quizzes with solution==
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*From instructor Jang, Summer 2015
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**[[Media:301Quiz1.pdf|Quiz 1. Linear and Time Invariant]] (pdf)
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**[[Media:301Quiz2.pdf|Quiz 2. Convolution of Two Rectangles]] (pdf)
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**[[Media:301Quiz3.pdf|Quiz 3. Continuous-Time Fourier Transform Exercise]] (pdf)
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**[[Media:301Quiz4.pdf|Quiz 4. Continuous-Time Fourier Transform Equation]] (pdf)
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**[[Media:301Quiz5.pdf|Quiz 5. Nyquist Sampling Theorem]] (pdf)
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**[[Media:301Quiz6.pdf|Quiz 6. Discrete-Time Fourier Transform Exercise]] (pdf)
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**[[Media:301Quiz7.pdf|Quiz 7. Sampling Theory]] (pdf)
 
----
 
----
 
==More Practice Problems==
 
==More Practice Problems==
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*On Fourier transform
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**[[Correct_CT_FT_1_ECE301Fall2008mboutin|Fourier transform problem]]
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**[[Homework_10_ECE301Fall2008mboutin|A mistake NOT TO REPEAT when computing Fourier transforms]]
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**[[Incorrect_CT_FT_periodic_signal_1_ECE301Fall2008mboutin|How NOT to take a Fourier transform]]
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*[[E_infinity_and_P_infinity_calculations_-_William_Owens_%28wtowens%29|Computing the energy and power of a CT signal: two examples]]
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*[[Ryan_Scott:_A_Laplace_example_from_class_ECE301Fall2008mboutin|Laplace transform example]]
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*[[ECE_301_Fall_2007_mboutin_Frequency_and_Impulse_Response_Example|Frequency and impulse response from diff. eq.]]
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*[[ECE_301_Fall_2007_mboutin_Convolution|Example of CT convolution]]
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*[[Exercise_1_ECE301Fall2008mboutin|Is this system time-invariant?]]
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*[[InverseZtransform|Inverse z-transform: summary of theory and practice examples with solutions]]
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*[[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)]]
 
----
 
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Click [[:Category:Problem_solving|here]] for a comprehensive list of all [[About_Rhea|Rhea]] pages in the "[[:Category:Problem_solving|problem solving]]" category.
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[[ECE301|Back to ECE301: "Signals and Systems"]]
 
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[[ECE301|Back]] to [[ECE301|Signals and Systems (ECE301)]]
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Latest revision as of 10:25, 22 January 2018


Practice Problems on Signals and Systems

(ECE301)



Collectively solved problems related to Signals and Systems


Problems from the official textbook (Oppenheim WIllsky)


Quizzes with solution


More Practice Problems


Back to ECE301: "Signals and Systems"

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