Digital Signal Processing 1

程序代写 CS代考

Digital Signal Processing 1

Lab course Winter Term

Assignment 1

1. FastFourierTransformation–FFT

  • ▪  Create a discrete sine signal with a frequency of 1Hz. Keep the sampling frequency and vector length variable.
  • ▪  Plot the signal vector in time domain. ▪ MATLABcommand:plot
  • ▪  Transfer the signal vector to the frequency domain and plot the result vector. ▪ MATLABcommand:fft
  • ▪  Hint: For better comparison of different plots use a single figure with various plots. ▪ MATLAB command: subplot

2. Single-sided linear spectrum – LS

  • ▪  Adapt the frequency domain vector plot in order to comply with the frequency and magnitude criteria.
  • ▪  Change the frequency of the initial sine signal from 1Hz to 1.05Hz.
    ▪ Which differences can be seen in the time and frequency domain plots? ▪ What effect emerges and how can it be minimized?
    ▪ Which purpose fulfill window functions in conjunction with the FFT?
  • ▪  Create a discrete third order harmonic sine signal with the fundamental frequency f and the first two overtones 2f and 3f.
    • ▪  Plot the signal in time and frequency domain.
    • ▪  Use different window functions for the harmonic signal and plot the various

      results in the time and frequency domain.

    • ▪  Discuss the differences.

      3. PowerSpectralDensity-PSD

  • ▪  Revise the fundamental mathematics for the power spectral density.
  • ▪  How does the linear spectrum plot have to be modified to get the power spectral density

    plot?

Applied Image & Signal Processing
Informationstechnik & System-Management 1/ 2 Salzburg University of Applied Sciences

Digital Signal Processing 1

Lab course Winter Term

Home Assignment: Spectral Density Estimation

  • ▪  Prerequisites
    • ▪  Make yourself familiar with MATLAB scripts and functions.
    • ▪  Do an academic research on the spectral density estimation methods of Bartlett,

      M.S. and Welch, P.D.

    • ▪  Be sure to know the differences between those two approaches.
  • ▪  Implement your own Welch method based MATLAB function.
    • ▪  Name the corresponding MATLAB script mywelch.m
    • ▪  Functionsignature[pxx]=mywelch(x)

      ▪ x – Input vector (time-domain, e.g. audio signal) [double]

      ▪ pxx – Output vector (spectral density estimation) [double]

    • ▪  Use the following header:

      % Date : <yyyy-mm-dd>
      % Author: <Firstname Lastname>
      % Course: AISE-M DSP1
      % Algorithm based on following literature:
      % <Name all references for your work. Use IEEE or APA citation style>
      % <e.g.> Welch, P. D. (1967). The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. IEEE Transactions on audio and electroacoustics, 15(2), 70-73.

  • ▪  Compare your implementation with the following MATLAB function: ▪ pwelch [Signal Processing Toolbox]
  • ▪  Write a test script testwelch.m, which generates or loads an appropriate time- domain signal. It should plot the power spectral density of the result vectors from mywelch and pwelch as a side-by-side comparison. Be sure to use correct axis labeling and plot titles.

    ▪ x-axis: Frequency scale (Hz)
    ▪ y-axis: Power spectral density (dB/Hz)

  • ▪  MATLAB files must have a header. Plots should be labeled and must have axis labeling.
  • ▪  Required upload

▪ testwelch.m ▪ mywelch.m

Applied Image & Signal Processing Informationstechnik & System-Management Salzburg University of Applied Sciences

2/ 2

Related Posts