MIT EECS: 6.003 Signal Processing lecture notes (Spring 2019)
Advanced Digital Signal Processing Labwork 1 · PDF fileAdvanced Digital Signal Processing...
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Advanced Digital Signal Processing Labwork 1 Technische Hochschule Mittelhessen 10/17 Prof. Dr.-Ing. Peter Schmitz labwork.doc Comparison of time continuous systems and their discretization 1. Build a continuous-time low pass system of order 2 with resonance frequency ω 0 = 1 s -1 and damping factor ϑ = 0.3: 1 s 2 s 1 1 ) s ( G 0 2 2 0 + ω ϑ + ω = . 2. Transform the system from no. 1 to a discrete-time system using a) H 0 -z-transform, b) bilinear z-transform, c) difference equation approach, d) impulse-invariant z-transform e) z-transform with pole-zero-matching. 3. Compare the poles and zeros of the 5 discrete-time systems of no. 2. 4. Compare the pulse-, step- and frequency-responses of the 6 systems (the original system 1 of no. 1 and the 5 discrete-time systems of no. 2). 5. Discuss the influence of sample-time T. Preparation at home (will be checked before the labwork starts) - Calulate the z-transfer-functions of the discrete-time systems from no. 2 manually. - Calculate the poles and zeros of all systems manually.
Transcript of Advanced Digital Signal Processing Labwork 1 · PDF fileAdvanced Digital Signal Processing...
Advanced Digital Signal Processing Labwork 1
Technische Hochschule Mittelhessen 10/17 Prof. Dr.-Ing. Peter Schmitz labwork.doc
Comparison of time continuous systems and their discretization 1. Build a continuous-time low pass system of order 2 with resonance frequency ω0 = 1 s-1 and
damping factor ϑ = 0.3:
1s2s11)s(G
0
22
0
+ω
ϑ+ω
= .
2. Transform the system from no. 1 to a discrete-time system using
a) H0-z-transform,
b) bilinear z-transform,
c) difference equation approach,
d) impulse-invariant z-transform
e) z-transform with pole-zero-matching.
3. Compare the poles and zeros of the 5 discrete-time systems of no. 2.
4. Compare the pulse-, step- and frequency-responses of the 6 systems (the original system 1 of no. 1 and the 5 discrete-time systems of no. 2).
5. Discuss the influence of sample-time T.
Preparation at home (will be checked before the labwork starts)
- Calulate the z-transfer-functions of the discrete-time systems from no. 2 manually.
- Calculate the poles and zeros of all systems manually.
Advanced Digital Signal Processing Labwork 2
Technische Hochschule Mittelhessen 10/17 Prof. Dr.-Ing. Peter Schmitz labwork.doc
Up- and downsampling 1. Generate a signal x = sin ωt + .5 * sin 3ωt + .3 * sin 5ωt with
- ω = 1000 s-1, - 10 samples per period for the highest signal-frequency and - 2048 samples at all.
2. Calculate the fourier-transform of the signal using the function fft, adjust amplitude- und frequency scaling and display the spectrum.
3. Increase the sampling rate by factor 3 (don’t use any special Matlab function, e.g. interpolate). Display the spectrum of the new signal and compare.
4. Filter the signal from 3 with a high order low pass and compare the spectrum again. Use the Matlab fdatool und try several filter designs.
5. Reduce the sample rate of the signal found in 4 by factor 5. Compare the spectrum again.
6. Discuss the results.
Preparation at home (will be checked before the labwork starts)
- What is the highest frequency in the signal x?
- What is the sample-time requested?
- Which is the highest calculated frequency of the spectrum of 2 and what is the resolution of it?
- Which amplitudes in the spectrum do you expect?
- Develop an algorithm for interpolation?
