 Discrete Fourier Transform
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WaveRider
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Registered Member #29
Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500
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Hi Andrew,
The c_n's are indeed complex in general. If your time-domain function is "even" about n=N/2, then the real transform will suffice. The DFT (FFT) assumes that your function is periodic in N, so interpolation will do nothing but bring you over into the next period between n=N->2*N-1..
If each time domain "bin" represents delta T and the total of N bins is N * delta T, then each "bin" in the frequency domain represents delta f = 1 / (N * delta T). The complete span of the transform N * delta f = 1 / delta T. (factors of 2 * pi may be added for angular frequency)..
Very fast FFTs can be implemented easily in integer arithmetic in DSPs and Harvard architecture uCs. In fact, the FFT can be implemented in hardware using FPGAs or ASICs with clock rates of 100s of MHz...
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