Calculating N for DFT - Signal Processing Stack Exchange most recent 30 from dsp.stackexchange.com 2019-11-12T16:31:35Z https://dsp.stackexchange.com/feeds/question/56788 https://creativecommons.org/licenses/by-sa/4.0/rdf https://dsp.stackexchange.com/q/56788 0 Calculating N for DFT pico https://dsp.stackexchange.com/users/41763 2019-04-19T02:41:06Z 2019-04-19T02:55:27Z <p>We want to compute an N-point DFT of a one-second duration compact disc (CD) audio signal x[n], whose sample rate is <span class="math-container">\$f_s = 44.1Khz\$</span> with a DFT sampling of 1 Hz.</p> <p>(a) What is the number of necessary x[n] time samples N? </p> <p>(b) what is the time duration of the x[n] sequence measured in seconds?</p> <hr> <p>I said:</p> <p><span class="math-container">\$f_s = 44100 hz\$</span> <span class="math-container">\$f_o = 1 hz\$</span> </p> <p>(a) <span class="math-container">\$N = f_s / f_o = 44100 / 1 = 44100?\$</span></p> <p>(b) <span class="math-container">\$T_s * N = (1/f_S) * N = (1/44100) * 44100 = 1 sec?\$</span></p> <p>Could I call <span class="math-container">\$f_0\$</span> the fundamental frequency of the DFT and assert that this frequency (1 hertz) corresponds exactly to a time period equal to the length of the x[n] sample range (1 second)? </p> <p>Is that the definition of the fundamental frequency of DFT...that its the frequency corresponding to the entire sample time period of x[n] of length N...which also happens to be the smallest frequency increment of DFT of which there are exact N frequency buckets that add up to the sampling frequency.</p>