University of Kansas
Electrical Engineering & Computer Science
EECS 360- Homework
Homework
Homework 1 Due 2/9/2021
Concept questions 2.1.1
Exercise 2.1.1
Exercise 2.1.2
Exercise 2.1.3
Homework 2 Due 2/11/2021
Participation activities
2.2.1: Phase angles and quadrants in the complex plane.
2.2.2: Complex number products and quotient
2.2.3: Complex algebra
Homework 3 Due 2/16/2021
Section 2.3 All participation activities
Challenge activities
2.3.1 1
2.3.3 2
Exercise 2.3.2
Exercise 2.3.4
Exercise 2.3.6
Exercise 2.3.9
Exercise 2.3.11
Section 2.4 participation activities
2.4.1
2.4.2
2.4.3
2.4.7
2.4.9
Exercise 2.4.1
Exercise 2.4.4
Exercise 2.4.6
Exercise 2.4.7
Homework 4
Due 2/18/2021
Homework 5 Due 2/25/2021
2.5 participation activity
2.5.1: Formation of unit step function.
2.5.2: Unit step function.
2.5.4: Ramp function.
2.5.5: Triangle waveform synthesized from ramps.
2.5.6: Rectangular (rect) function.
2.5.8: Impulse function.
2.5.9: Sampling property of the impulse function.
2.5.10: Time-scaling of impulse function sampling integrals.
2.5.11: Exponential function.
2.5.12: Exponential functions.
Challenge activities
2.5.1: Nonperiodic waveforms 3.
Exercise 2.5.3
Exercise 2.5.4
Exercise 2.5.8
Exercise 2.5.12
2.6 participation activity
2.6.1: Energy or power signals?
2.6.2: Energy or power or neither?
2.6.3: Power and energy in sums of signals.
Exercise 2.6.1
Exercise 2.6.3
3.1 participation activity
3.1.1: Properties of square function.
3.1.2: Linear or not?
3.1.5: Is the system time invariant?
Concept questions 3.1.1 Question 1.
Exercise 3.1.1 a, b, e, g
Homework 6 Due 3/4/2021
3.2 participation activity
3.2.1: Measuring impulse response via a narrow pulse input.
3.2.2: Determining impulse response as the derivative of the step response.
Concept questions 3.2.1
Exercise 3.2.1
Exercise 3.2.5
3.3 participation activity
3.3.1: Methods to implement convolution.
3.3.2: Convolution of two rectangular pulses.
3.3.3: Convolution of two rectangular pulse.
3.3.4: Convolution of functions with step functions
3.4 participation activity
3.4.1: RC circuit response to rectangle pulse, graphical and analytical convolution.
3.4.2: Review of analytical convolution: rectangle and triangle.
3.4.3: Graphical convolution of rectangular pulse input and triangle impulse response.
Exercise 3.4.1
Exercise 3.4.4
3.5 participation activity
3.5.1: Convolution properties.
3.5.2: Convolution of two delayed rectangular pulses, using the properties.
3.5.3: Convolution properties.
3.5.4: Common convolutions.
3.5.5: Using convolution properties.
3.5.6: Finding the area under a decaying exponential curve
Exercise 3.5.1
Exercise 3.5.4
3.6 participation activity
3.6.1: BIBO stability and causality.
3.6.2: BIBO stability.
3.6.3: BIBO stability for complex exponential (sinusoidal) signals.
Exercise 3.6.1
Exercise 3.6.4
3.7 participation activity
3.7.1: Frequency response function and output from sinusoidal input.
3.7.2: Time-domain response and frequency response pairs
3.7.3: Is this system sinusoidal response LTI (Linear Time Invariant)?
challenge activity
3.7.1: LTI sinusoidal response.4
Exercise 3.7.1
Exercise 3.7.2
Exercise 3.7.3
Exercise 3.7.4
Exercise 3.7.8
Exercise 3.7.10
Exercise 3.7.11
Homework 7 Due March 18, 2021
4.1 participation activity
4.1.1: Time to phasor domain transform examples.
4.1.3: Phasor technique to solve differential equations having sinusoidal inputs.
Exercise 4.1.1
Exercise 4.1.5
4.2 participation activity
4.2.1: Fourier series analysis technique.
4.3 participation activity
4.3.1: Fourier series harmonics
4.4 participation activity
4.4.2: Sine/cosine Fourier series for sawtooth wave.
4.4.3: Line spectra of triangle wave.
4.4.4: Amplitude/phase Fourier series for sawtooth wave.
4.4.5: Fourier series coefficients. .
4.4.8: Effect of number of Fourier terms used to represent a signal.
Exercise 4.4.3
Exercise 4.4.12
Exercise 4.4.14
Homework 8 Due March 25, 2021
4.5 participation activity
4.5.1: Fourier series analysis for RC circuit with triangle wave input.
4.5.3: Fourier analysis of RC circuit, half-wave rectified sine input.
4.6 participation activity
4.6.1: Average power of sinusoidal signals.
4.6.2: Average power of sum and product of sinusoids.
4.6.3: Parseval's theorem for Fourier series.
4.6 challenge activity
4.6.1: Parseval's theorem for periodic waveforms 6.
Exercise 4.6.2
Exercise 4.6.3
4.7 participation activity
4.7.1: Fourier transform and sinc
4.7.2: Rectangular pulse frequency spectrum.
4.7.3: Calculating Fourier transforms of constants and exponentials.
Exercise 4.7.1
Exercise 4.7.2
Exercise 4.7.3
Exercise 4.7.6
Exercise 4.7.9
Homework 9 Due April 1, 2021
4.8 participation activity
4.8.1: Time scaling property of the Fourier transform.
4.8.2: Fourier transform time scaling.
4.8.3: Fourier transforms of shifted impulse functions.
4.8.4: Time shift property of the Fourier transform, and phase.
4.8.6: Fourier transform pairs.
4.8.7: Fourier transforms of step functions and exponentials.
4.8.8: Deriving the Fourier transform modulation property, using the frequency-shift property.
4.8.9: Fourier transform properties: derivative, modulation, and convolution.
4.8.10: Reviewing Fourier transform properties.
Exercise 4.8.1
Exercise 4.8.5
Exercise 4.8.9
Exercise 4.8.10
4.9 participation activity
4.9.1: Time-domain energy computations for non-periodic signals.
4.9.2: Parseval's theorem and energy spectral density.
4.9 challenge activity
4.9.1: Parseval's theorem for Fourier transforms.7
Exercise 4.9.2
4.10 participation activity
4.10.2: Attributes of Fourier transforms.
4.12 participation activity
4.12.1: Fourier circuit analysis.
4.12.2: RC circuit analysis via Fourier transform, with exponential input.
4.12.3: RC circuit analysis via Fourier transform, for cosine input
CTFT Problems.
Homework 10 Due April 6, 2021
5.2 participation activity
5.2.1: Lowpass and highpass magnitude spectral responses.
5.2.2: Bandpass and bandreject magnitude spectral responses.
5.2.3: RC circuit lowpass filter (capacitor output).
5.2.4: RC circuit highpass filter (resistor output).
5.2.6: Ratio to dB conversions.
5.2.7: dB to voltage ratio conversions.
Exercise 5.2.1
Exercise 5.2.5
Exercise 5.2.6
5.3 participation activity
5.3.1: Examples of bandpass filter responses and Q factor.
5.3.2: Designing a bandpass filter for resonant frequency MHz and factor .
5.3.5: RLC highpass filter.
5.3.7: First order lowpass filter transmission spectrum.
challenge activity 5.3.1: Bandpass filters.
Exercise 5.3.1
5.4 participation activity
5.4.1: Brick-wall lowpass filter response to odd square-wave input.
5.4.3: Brick wall filter impulse responses.
5.4.4: Brick wall bandpass response to odd squarewave.
5.4.5: Brick wall bandpass response to rectified sine wave
Exercise 5.4.1
Analog Filtering
Homework 11 Due April 8, 2021
5.5 participation activity
5.5.1: Modulation terminology.
5.5.2: AM and DSB Spectra, with envelope detection.
5.5.3: DSB and AM.
5.5.4: FDM total bandwidth.
5.5.5: AM radio station bandwidth.
Exercise 5.5.1
Exercise 5.5.3
5.6 participation activity
5.6.1: Nyquist sampling rate.
5.6.2: Sampling theory.
5.6.4: Sampling terminology.
5.6.5: Sampling rates.
challenge activity 5.6.1: Sampling theorem.8
Exercise 5.6.2
Exercise 5.6.3
Exercise 5.6.4
Exercise 5.6.7
Homework 12 Due April 22, 2021
6.1 participation activity
6.1.1: Transformations for Digital Signal Processing (DSP)
6.1.2: Discrete-time signal transformations.
6.1.3: Discrete-time signal durations and transformations.
6.2 participation activity
6.2.1: Sampling rate and discrete-time period and frequency
6.2.2: Discrete-time periodic parameters.
6.2.3: Periodic parameter values.
6.2.4: Periodic continuous-time vs. discrete-time functions.
6.2.5: Discrete sinusoids.
challenge activity
6.2.1: Discrete-time signal functions
Exercise 6.2.1
Exercise 6.2.2
6.3 participation activity
6.3.1: Discrete-time system terminology
6.3.2: ARMA difference equations.
6.4 participation activity
6.4.1: Properties of discrete-time systems, part one.
6.4.2: Properties of discrete-time systems, part two.
6.4.3: Impulse response of MA (moving average) system.
6.4.4: Step response of moving average system.
6.4.5: ARMA system, impulse and step responses.
6.4.6: ARMA system, |p|<1 impulse and step responses.
6.4.7: Discrete-time system stability.
challenge activity
6.4.1: Properties of discrete-time LTI systems.9
Exercise 6.4.1
Exercise 6.4.2
Exercise 6.4.3
6.5 participation activity
6.5.1: Example: delayed-impulses convolution method.
6.5.2: Delayed-impulses convolution, input
6.5.3: Discrete-time convolution via delayed impulses.
6.5.4: Graphical or textual sliding convolution.
6.5.5: Graphical convolution process.
6.5.6: Graphical convolution values.
challenge activity
6.5.1: Discrete-time convolution. 10
Exercise 6.5.1
Exercise 6.5.2
Exercise 6.5.5
Homework 13 Due April 27, 2021
6.6 participation activity
6.6.1: z-transform definition.
6.6.2: z-transform of a finite duration sequence.
6.6.4: Visualizing the z-transform.
6.6.6: z -transform of sinusoids.
6.6.7: z-transforms of some sinusoids.
6.6.8: z-transform pairs.
Exercise 6.6.1
6.7 participation activity
6.7.2: Convolution property of the z-transform
6.7.3: z-transform properties.
6.7.4: z-transform properties-part 2.
challenge activity
Properties of the z-transform (1). 11
Exercise 6.7.1
6.8 participation activity
6.8.1: Inverse z-transforms.
Exercise 6.8.1 a & b
Exercise 6.8.2 a
6.9 participation activity
6.9.1: Difference equation, block diagram, transfer function, and impulse response.
6.9.2: Discrete LTI system transfer function, impulse response, and difference equation.
6.9.3: Deriving the transfer function from a difference equation.
Homework 14 Due April 29, 2021
6.10 participation activity
6.10.1: Transfer function and pole location vs. impulse response
6.10.2: Stability and transfer function poles.
6.10.3: Transfer function, poles, and stability.
challenge activity
6.10.1: BIBO stability of H(z) 12
Exercise 6.10.1
Exercise 6.10.3
Exercise 6.10.4
6.11 participation activity
6.11.1: Frequency response of a lowpass filter.
6.11.2: Discrete-time system frequency response.
6.11.3: Example: Input-Output Pair to Other Descriptions.
Exercise 6.11.1
Exercise 6.11.2
6.12 participation activity
6.12.1: Moving a zero along the unit circle.
6.12.2: Effect of moving a zero toward the center of the unit circle.
6.12.3: Moving conjugate poles towards the center of the unit circle.
6.12.4: Conjugate pole angles vs. frequency response.
6.12.5: Pole zero placement vs. frequency response.
6.12.6: Lowpass filter poles, zeroes, transfer function.
6.12.7: Highpass filter.
6.12.8: Bandpass filters.
6.12.9: Bandreject filters.
Exercise 6.12.1 (You can use
Transfer Function Analysis by Manipulation of Poles and Zeros
)
Exercise 6.12.2 (You can use
Transfer Function Analysis by Manipulation of Poles and Zeros
)
6.13 participation activity
6.13.1: 250Hz notch filter design.
6.13.2: Discrete-time notch filters.
Exercise 6.13.4
Filtering digital signals
Problems 1-8
Homework 15 Due May 4, 2021
6.17 participation activity
6.17.2: Computing a DFT.
6.17.3: DFT of a finite sequence.
6.17.4: DFT of a finite sequence, without zero-padding.
6.17.5: Discrete Fourier transforms.
6.17.6: Cyclic convolution, graphical and textual methods.
6.17.7: DFT and convolution.
6.17 challenge activity
6.17.1: Discrete Fourier transform (DFT) 13.
Exercise 6.17.1
Exercise 6.17.3
6.18 participation activity
6.18.1: Data window properties.
6.18.2: Data window equations.
6.18.4: Cosine signal spectra with rectangular and Hamming data windows.
6.18.5: Rectangular and Hamming data windows reveal presence of cosine signal components.
6.18.6: Rectangular and Hamming data windows with a small-magnitude cosine signal.
6.18 challenge activity
6.18.1: Data windows.14
6.19 participation activity
6.19.1: Padding data arrays for the FFT.
6.19.3: FFT and lowpass filtering.
6.19.4: Filtering via thresholding.
Exercise 6.19.3
6.20 participation activity
6.20.1: Discrete filter terminology.
6.20.2: Lowpass filter designed by windowing.
6.20.4: Window design of FIR differentiator, with rectangular window.
6.21 participation activity
6.21.5: IIR filter design.
DFT Problems
Author
Victor S. Frost
,
vsfrost@ku.edu