Signal Processing for Communication Systems
Key focus: Window function smooths the observed signal over the edges. Analysis of some important parameters to help select the window for an application. Spectral leakage As we know, the DFT operation can be viewed as processing a signal through a set of filter banks with bandwidth Δf centered on the bin (frequency) of interest … Read more
Key focus: Equivalent noise bandwidth (ENBW), is the bandwidth of a fictitious brick-wall filter that allows same amount of noise as a window function. Learn how to calculate ENBW in applications involving window functions and FFT operation. FFT and spectral leakage As we know, the DFT operation can be viewed as processing a signal through … Read more
The Parseval’s theorem (a.k.a Plancherel theorem) expresses the energy of a signal in time-domain in terms of the average energy in its frequency components. Suppose if the x[n] is a discrete-time sequence of complex numbers of length N : xn={x0,x1,…,xN-1}, its N-point discrete Fourier transform (DFT)[1] : Xk={X0,X1,…,XN-1} is given by The inverse discrete Fourier … Read more
In the previous post, Interpretation of frequency bins, frequency axis arrangement (fftshift/ifftshift) for complex DFT were discussed. In this post, I intend to show you how to interpret FFT results and obtain magnitude and phase information. Outline For the discussion here, lets take an arbitrary cosine function of the form \(x(t)= A cos \left(2 \pi … Read more
Key focus: Interpret FFT results, complex DFT, frequency bins, fftshift and ifftshift. Know how to use them in analysis using Matlab and Python. Four types of Fourier Transforms: Often, one is confronted with the problem of converting a time domain signal to frequency domain and vice-versa. Fourier Transform is an excellent tool to achieve this … Read more