Discrete Fourier Transform (DFT) is the sampled form of DTFT(Discrete Time Fourier Transform).
It was realized on plotting the magnitude spectrum, that on appending zeros at the end of the input signal, gives us a better spectrum, on which
1. Reduces error
2. Frequency spacing decreases
3. Spectrum resolution increases. If we expand the original time domain signal, the DFT output gets compressed and vice versa.
1. Reduces error
2. Frequency spacing decreases
3. Spectrum resolution increases. If we expand the original time domain signal, the DFT output gets compressed and vice versa.
To perform DFT, we need to perform [4N(^2)] real multiplications and [4N(^2) - 2N] real additions. For N=4, these values are 240 and 256 respectively. Thus, DFT requires a lot of mathematical computation which renders it to be quite slow for practical applications. A better way is to use Fast Fourier Transform which we will look into in the third experiment.
Zero padding improves resolution.
ReplyDeleteYes, it does, as mentioned in point 3
ReplyDeleteDFT can be used to find transfer fumction
ReplyDeleteYes, transfer function can be obtained in transform domain!
DeleteBut DFT always assumes periodic signals
ReplyDeleteYes, periodic signals have discontinuous spectrum
DeleteDFT is slower method than FFT.
ReplyDeleteYes, FFT is faster
DeleteFFT is faster
ReplyDeleteYes, FFT is faster
DeleteThis is because FFT uses parallel processing!
DeleteDFT is a generalized complex computation method for frequency domain analysis. Here, complex numbers are used as a signal is represented as a sum of sines and cosines which have a mutual 90 degree phase shift.
ReplyDeleteDFT is obtained by sampling DTFT
ReplyDeleteDFT results are periodic
ReplyDeleteDFT is slow compared to FFT
ReplyDeleteDFT was originally used for frequency domain analysis. Using a few properties of sinusoidal signals,FFT was develped.
ReplyDelete