Four different tasks in regard to digital signal processing are introduced and solved. The code as well as the output will be given.
Inhaltsverzeichnis
- The following continuous-time signal is sampled in the time interval of t = 0 ≤t< 40 *10^-3 sec and fs = 25000 Hz - x(t) = sin(2×1000t) + 3cos(2л × 2000t) — 5sin(2л ×625t) + 2cos(2π ×1625t). Find the DFT of the resultant discrete-time signal and plot its magnitude versus the "actual" frequency. Explain what you see in the graph. (You can use fft command in MATLAB to find the DFT of the signal)
- Let's repeat the above procedure in the time interval of t = 0 ≤t < 38 * 10 ^-3 Sec. Why the DFT magnitudes plot is different compared to the one obtained in the previous question? Explain. (This effect is called: spectral leakage!)
- Consider the following finite length signals:
x1 = [1 21-26 0 1 -1 2];
x2 = [1 -2 4 7 1];
They both start at n = 0.
- Find the convolution of the signals using the “conv” function in MATLAB.
- Find the convolution of the signals using the DFT and IDFT method. Employ 16-point DFT and IDFT.
- Show that results of part (a) and part (b) are identical (ignore the padded zeros at the end of the signal that you obtained in part (b)).
Zielsetzung und Themenschwerpunkte
This document aims to explore the concept of Discrete Fourier Transform (DFT) and its application in signal processing. It delves into the analysis of continuous-time signals using DFT and investigates the phenomenon of spectral leakage. The document also demonstrates the convolution of finite length signals using both the "conv" function and the DFT/IDFT method.
- Discrete Fourier Transform (DFT)
- Spectral Leakage
- Convolution of Signals
- DFT and IDFT Method
- Signal Processing Applications
Zusammenfassung der Kapitel
The first chapter focuses on the DFT of a continuous-time signal sampled at a specific frequency. It analyzes the magnitude spectrum of the DFT and explains the observed patterns. The second chapter explores the concept of spectral leakage, which occurs when the signal analyzed does not contain an integer number of periods. It compares the DFT magnitudes obtained in the first and second chapters and explains the differences. The third chapter delves into the convolution of finite length signals using both the "conv" function and the DFT/IDFT method. It demonstrates the equivalence of the results obtained using both methods.
Schlüsselwörter
The key terms and focus themes of the text include Discrete Fourier Transform (DFT), spectral leakage, convolution of signals, DFT and IDFT method, signal processing applications, continuous-time signals, discrete-time signals, frequency domain analysis, time domain analysis, and MATLAB programming.
- Quote paper
- Pragnesh Patel (Author), 2014, Tasks for Digital Signal Processing with Solution, Munich, GRIN Verlag, https://www.grin.com/document/284206
