Search Results

}(a_1 x_1[n] + a_2 x_2[n]) = a_1\mathrm{FFT}(x_1[n]) + a_2\mathrm{FFT}(x_2[n]) $$ DFT of the unit impulse: A time-domain signal equal to the Kronecker delta function is applied to the input of the … The authors of the paper assert that these tests are sufficient to validate the correctness of an FFT implementation. …

Instead of having a hard edge between the image data of interest and the background, you could use a two-dimensional tapered window function, as is often done in spectral analysis. You might start by …

This can be a valid approach. You're observing a very practical issue that arises often when using fixed-point (i.e. integer) arithmetic (although it can happen in floating-point also). When the numer …

However, even the seminal FFT technique, the Cooley-Tukey algorithm, generically factorizes the FFT size into smaller numbers, not just powers of 2. … Using a good FFT library, you'll get the best performance if your FFT size can be factored into a number of small prime factors. …

For the Cooley-Tukey FFT, this is often quoted as $5N \log N$ scalar operations (real multiplies and additions). This is a pretty straightforward idea. …

For a real signal, content at the negative frequencies generated by using the DFT is redundant. This is due to the well-known property of real signals with respect to the Fourier transform family: the …

What you seem to want is the phase response of the device that your optical system is passing through. Based on that, your high-level approach makes intuitive sense overall; I'm not sure why you chose …

There is no single "time instant" associated with a short-time Fourier transform. As you noted, if you perform a DFT on data collected from $t = 0$ to $t = 64$, then there isn't a single point in time …

Translating a signal in frequency before performing an FFT cannot improve the optimum probability of detection due to the principle of reversibility in detection theory; since shifting a signal in frequency …

If you're concerned with doing spectral analysis on a signal with a large DC component, and you want to suppress that DC peak, then a window function is not what you want. As some other answers noted, …

You see one at index 8 because MATLAB's indexing is one-based, not zero-based as the equations that describe the DFT are. You get two spikes because your input signal is real and is therefore conjugat …

One thing that comes to mind is that a linear predictor can be implemented using the LMS algorithm, and the LMS algorithm can be implemented in block fashion using FFTs (see Chapter 7 of Haykin's Adap …

The forward FFT result is passed through another function DSPF_sp_icfftr2_dif(), which is described as a radix-2 decimation-in-frequency inverse FFT. … It expects its input in bit-reversed order (which it is, as the input is the output of the forward FFT above, which was in bit-reversed order). …

A little Googling came up with this reference, which indicates that the impulse response for a Taylor window is: $$ h[n] = 1 + 2 \sum_{m=1}^{\tilde{n}-1} F_m \cos\left(\frac{2\pi m}{N} \left(n-\frac{ …

You're running into a property of the DFT that is usually used in the opposite direction: stuffing zeros between samples in one domain results in replication of the entire sequence in the opposite dom …