Discrete Fourier Transform was studied in our lab by taking three cases. The three cases were analysed on the basis of the frequency spectra obtained in each case. The first case of 4-point signal gave a 4- point DFT signal. The second case of 8 point signal was taken with the same 4 points as the first four elements and the last 4 elements were taken as zero. The DFT obtained was had less frequency spacing and hence less approximation was done to plot the spectrum. The third case taken involved an 8- point signal alternate input elements and zeros, The DFT obtained in this case was an 8- point signal with the first four elements getting repeated in the last four element block. Thus, we concluded that expansion of the signal in discrete time domain led to compressed DFT signal in frequency domain. Adding to this, DFT was found to have heavy computation, which made it slower.
Its basically frequency sampling of DTFT and it is required if we want to store the results in memeory of the processor.DFT results are always periodic.
ReplyDeleteDiscrete Fourier Transform is like sampling DTFT. Hence, analysis can be done on any particular value of frequency.
ReplyDeleteApplications of DFT algorithms:
ReplyDelete1)Human speech and hearing use signals with this type of encoding.
2)DFT can find a system's frequency response from the system's impulse
response, and vice versa is also possible. This allows systems to be analyzed in the
frequency domain, just as convolution allows systems to be analyzed in the time domain. 3)DFT can be used as an intermediate step in more elaborate signal processing techniques. The classic example of this is FFT convolution, an algorithm for convolving signals that is hundreds of times faster than conventional methods.
Good content
ReplyDeletewell written
ReplyDeleteInformative content
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