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Digital Signal Processing. Discrete Fourier Transform. Discrete Fourier Transform. Inverse Discrete Fourier Transform. Properties of DFT. DFT has the same number of datapoints as the signal The signal is assumed to be periodic with a period of N
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Discrete Fourier Transform Discrete Fourier Transform Inverse Discrete Fourier Transform
Properties of DFT • DFT has the same number of datapoints as the signal • The signal is assumed to be periodic with a period of N • X[k] corresponds to the amplitude of the signal at frequency f=k/(NT) • The frequency resolution of the DFT is Df=1/(NT), i.e. the # of samples determines the frequency resolution
Steps for Calculating DFT • Determine the resolution required for the DFT, establish a lower limit on the # of samples required, N. • Determine the sampling frequency to avoid aliasing • Accumulate N samples • Calculate DFT
Digital Filtering a1*y(n) = b1*x(n) +b2*x(n-1) + ... + bnb+1x(n-nb) - a2*y(n-1) - ... – ana+1*y(n-na) A=[a1,a2,..., ana+1] Filter parameters B=[b1,b2,..., bnb+1] X=[x(n-nb),..., x(n-1), x(n)]: input signal Y=[y(n-na),..., y(n-1), y(n)]: filtered signal
Ideal Filters • Low pass filter • High pass filter • Bandpass filter • Bandstop filter
Butterworth filter: Common Filters • Chebyshev filter:
