EE432 Spring 2011: Instructional
Objectives by Chapter
Chapter 1: Crash Course in DSP
1. State the definitions of analog and digital signals.
2. Give examples of analog signals and digital signals.
3. Describe the steps involved in A/D conversion, and the following terms: aliasing, quantization error, zero-order hold.
4. Define fundamental frequency, harmonic frequencies, and filter cutoff frequencies.
Chapter 2: A/D and D/A
1. State the Nyquist sampling theorem.
2. Given sinusoidal signals and a sample rate, determine if aliasing occurs and if so, what frequencies are present after sampling.
3. Describe the purpose of an anti-imaging (anti-aliasing filter).
4. Given the parameters of an input analog signal, design an A/D, including sample rate and number of bits to achieve a desired resolution. Create a quantization table using these parameters.
5. Determine the max quantization error, signal-to-quantization noise in dB, and the dynamic range in dB.
6. Given a plot of an analog signal and the parameters of an A/D converter (sample rate, resolution, # bits), sketch the digital approximation to the analog signal out of the A/D. Determine the resulting bit rate and bit pattern.
7. Given a digital bit pattern and the parameters of an A/D, determine the digital waveform out of a D/A.
Chapter 3: Digital Signals
1. Given samples of a digital signal, determine the result of time-scaling the signal.
2. Given a plot of a digital signal, write an expression for the signal in terms of impulse functions.
3. Express the following functions in equation form as well as on plots: impulse function, step function, power and exponential functions, digital sinusoids, and composite functions.
Chapter 4: Difference Equations and Filtering
1. For a digital filter, define: roll-off, gain, pass band, stop band, and bandwidth (-3dB). Given a plot of a filter's frequency response, determine those values for the filter.
2. Determine if a digital filter is linear, time-invariant, and causal.
3. Describe the differences between a recursive and nonrecursive filter in terms of the difference equation.
4. Using the table method, determine the output of a recursive filter for a given input.
5. Use superposition to determine the output of a nonrecursive filter for a given input.
6. Given a difference equation, draw a block diagram of the filter using delays, multipliers and summers. Given a block diagram, write the associated difference equation.
7. Define FIR and IIR. Use the table method to determine the impulse response for an FIR and an IIR filter.
8. Determine the step response of a filter.
Chapter 5: Convolution and Filtering
1. Determine the convolution result between a digital signal and a filter's impulse response.
2. In convolution, describe what is meant by boundary effects, transient behavior, and steady state behavior.
3. Write the difference equation for a moving average filter as a recursive filter, and also as a nonrecursive filter.
Chapter 6: Z-Transforms
1. Define the terms Z-transform (ZT) and region of convergence (ROC).
2. Given a digital signal, determine its ZT and ROC.
3. Given the difference equation for a recursive or nonrecursive filter, determine its transfer function.
4. Using a table of ZTs, determine the ZT and ROC for a given signal.
5. Given a filter's transfer function, determine its impulse response and vice-versa.
6. Determine the overall transfer function for a system comprised of series and/or parallel filters.
7. Use long division to convert a proper transfer function into a strictly proper expression.
8. Determine the inverse ZT of a signal using long division, partial fraction expansion, or ZT tables as directed.
9. Given a filter's transfer function, determine and plot its poles and zeros, and evaluate its stability.
10. Given a filter's transfer function, determine its impulse response and step response.
Chapter 7: Fourier Transforms and Filter Shape
1. Calculate the discrete-time Fourier transform (DTFT) for a given signal.
2. State the relationship between a filter's frequency response and its impulse response.
3. Given a transfer function or difference equation, determine a filter's frequency response.
4. Determine the magnitude and phase effects of a digital filter on an input sinusoid.
5. Given a difference equation, find and sketch the frequency response of a system (magnitude response and phase response). Plot gain in dB and phase in degrees or radians as directed.
6. Convert between digital and analog frequency.
7. Deduce the filter shape from poles and zeros of a filter.
8. Using filter shape, determine the type of filter: low pass, high pass, band pass, band stop, comb, etc.
Chapter 8: Digital Signal Spectra
1. Given a sample rate and samples of a nonperiodic signal, determine the magnitude and phase spectrum of the digital signal.
2. Determine the magnitude and phase spectrum of a periodic signal, such as a square wave.
Chapter 9: FIR Filters
1. Define the term phase distortion.
2. Describe the method of approximating an ideal low pass filter, and calculate the pass band ripple, stop band ripple, transition width and cutoff frequency.
3. State the purpose of using windows.
4. Design a windowed low pass FIR filter using the design procedure, given the filter specifications (pass band edge, stop band edge, stop band attenuation, sample frequency).
5. Use an equivalent low pass filter to design a band pass or high pass filter, given the filter specifications.
6. Design a band stop filter using a parallel low pass and high pass filter.
7. Design an equiripple FIR filter.
8. Describe the hazards associated with the design of practical FIR filters.
9. Use MATLAB to aid in filter design, and perform signal filtering using MATLAB.
Chapter 10: IIR Filters
1. Use the bilinear transformation to convert between an analog and a digital filter.
2. Design a low pass Butterworth filter using the design procedure, given the filter specifications (-3dB bandwidth, sample rate). Choose the order of the filter based on the attenuation required at a specified frequency.
3. Use MATLAB to aid in filter design, and perform signal filtering using MATLAB.
4. Design a system to recover DTMF tones using IIR filters in MATLAB.
5. Describe the hazards associated with the design of practical IIR filters.
Chapter 11: DFT and FFT Processing
1. Calculate the discrete Fourier transform (DFT) of an given signal. Plot the magnitude and phase of the DFT.
2. Relate the DFT to the DTFT and the Fourier transform.
3. Discuss the effects of number of samples on the DFT/FFT. Define the terms spectral leakage and ringing.
4. Analyze a signal using a spectrogram.
5. Relate the FFT to the DFT.
6. Analyze a signal in MATLAB using an FFT.
Chapter 14: Signal Processing
1. Describe the processes of: oversampling, decimation, zero insertion, interpolation, dithering, companding.
2. Apply digital signal processing techniques to voice signals, music, sonar and seismic signals.