In this experiment we have verified the Discrete Fourier Transform of a signal by executing a C- program for the same wherein arrays have been used to store real and imaginary parts of the signal.
This signal is manipulated (such as zero padded or expanded form of the same signal) in different ways through this experiment and for each situation we have studied the result.
DFT is the frequency sampled version of DTFT hence giving periodic results.
We also plot its magnitude spectrum by approximation for both 4pt and 8pt (zeros appended to 4pt sequence) signals as well as expanded signal by adding zeros between the for 4pt sequence.
We observe that expansion in time domain gives a compressed spectrum in frequency domain and by finding number of additions and multiplications required we concluded that DFT is computationally slow.
This signal is manipulated (such as zero padded or expanded form of the same signal) in different ways through this experiment and for each situation we have studied the result.
DFT is the frequency sampled version of DTFT hence giving periodic results.
We also plot its magnitude spectrum by approximation for both 4pt and 8pt (zeros appended to 4pt sequence) signals as well as expanded signal by adding zeros between the for 4pt sequence.
We observe that expansion in time domain gives a compressed spectrum in frequency domain and by finding number of additions and multiplications required we concluded that DFT is computationally slow.
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ReplyDeleteWell written!
ReplyDeleteThank you keshvi
DeleteNumber of arithmetic operations required is more than that of FFT
ReplyDeleteYes.. as FFT decomposes the input signal before calculations
DeleteIt is slower than FFT as computations are more.
ReplyDeleteTrue
Deletethe twiddle factors are periodic
ReplyDeleteYes indeed
DeleteSo periodicity is determined by twiddle factor?
ReplyDeleteYes it is
DeleteSpacing between the values reduces as the value of N increases. By appending the input sequence by zeros the resolution error reduces.
ReplyDeleteBy appending more zeros, missing values in the less point DFT are present in the DFT with more points
Delete