3/20/2023 0 Comments Hamming window igor pro![]() (13-11) can be performed in hardware with two binary right shifts by a single bit for a = 0.5 and two shifts for each of the two b/2 = 0.25 factors, for a total of six binary shifts. ![]() They're both 0.5, and the multiplications in Eq. The neat situation here are the frequency-domain coefficients values, a and b, for the Hanning window. (In this case, we called our windowed results Xthree-term(m) because we're performing a convolution of a three-term W(m) sequence with the X(m) sequence.) (13-11), requiring 4N additions and 3N multiplications, to the unwindowed N-point FFT result X(m) and avoid having to perform the N multiplications of time domain windowing and a second FFT with its Nlog2(N) additions and 2Nlog2(N) multiplications. To compute a windowed N-point FFT, Xthree-term(m), we can apply Eq. Then frequency-domain windowing for the mth bin of the unwindowed X(m) is as follows: (13-8).įor example, let's say the output of the mth FFT bin is X(m) = am + jbm, and the outputs of its two neighboring bins are X(m–1) = a–1 + jb–1 and X(m+1) = a+1 + jb+1. This frequency domain convolution process is equivalent to multiplying the input time data sequence by the N-valued window function w(n) in Eq. This means that a times the mth bin output, minus b/2 times the (m–1)th bin output, minus b/2 times the (m+1)th bin output will minimize the sidelobes of the mth bin. Notice that the two translated sin(x)/x functions have side lobes with opposite phase from that of the center sin(x)/x function. General cosine window frequency response amplitude. Their amplitudes are shown in Figure 13-10.įigure 13-10. (13-10) merely results in the superposition of three sin(x)/x functions in the frequency domain. (13-8) isĮquation (13-10) looks pretty complicated, but using the derivation from Section 3.13 for expressions like those summations we find that Eq. Looking at the frequency response of the general cosine window function, using the definition of the DFT, the transform of Eq. They both have the general cosine function form ofįor n = 0, 1, 2. Recall from Section 3.9 that the expressions for the Hanning and the Hamming windows were wHan(n) = 0.5 –0.5cos(2pn/N) and wHam(n) = 0.54 –0.46cos(2pn/N), respectively. We can perform the FFT of the unwindowed data and then we can perform frequency-domain windowing on that FFT results to reduce leakage. In this situation, we don't have to perform two separate FFTs. There are times when we need the FFT of unwindowed time domain data, while at the same time we also want the FFT of that same time-domain data with a window function applied. There's an interesting technique for minimizing the calculations necessary to implement windowing of FFT input data to reduce spectral leakage.
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