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What’s New in this Release:
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* The focus is now on user-friendliness and easy of use,
* Improved ‘add new file’ menu,
* A more robust encryption of files,
* The tool has been ported to the use of a graphic user interface,
* Windows 10 is supported now,
* A bunch of minor bug fixes and improvements,
* It can now (maybe) still work with Windows 2000/XP..
* Basic audio Player that will play your music files and convert them to MP3, AIFF, WAV or AAC formats,
* The audio Player can copy music tracks to the clipboard for you,
*.MP3 or.WAV audio files can be converted to.WMA format,
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*.AIFF and.WAV audio files can be converted to.MP3 or.WMA format,
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￭ Press down arrow keys to change the mode
￭ Press up arrow keys to change the speed
￭ Press ESC to exit the menu
￭ Press F11 to activate the menu
￭ Mouse wheel to scroll through menu items
￭ Press Enter to select item
￭ Press Esc to quit the program
￭ Press Z to rotate the screenQ:
Fourier coefficients in filter design
Suppose I have a signal $x(t)$ that I want to decimate. Then I can define the decimated signal $\hat{x}(t)$ by $x(n)=\hat{x}(nT)$. The Fourier coefficient of the decimated signal is given by
$$\hat{x}_k=\frac{1}{N}\sum_{n=0}^{N-1} x(n) \exp(-i2\pi k n/N).$$
If I want to design a filter $h(t)$ with $\hat{h}(k)$ as the Fourier coefficient of the filter I can do so by defining the filter as
$$h(t)=\frac{1}{N}\sum_{n=0}^{N-1} x(n) \exp(-i2\pi k n/N)$$
My question is this: is it necessary that $h(t)$ be decimated in order to have $\hat{h}(k)$ as the Fourier coefficient of the filter $h(t)$? If $h(t)$ is not decimated, can I still get the coefficients by decimating $h(t)$?
A:
It is possible to keep the time samples of a signal $x(t)$ the same, but at the cost of reduced frequency resolution. The reason is that the discrete-time Fourier transform of $x(t)$ at frequency $k$ is given by $\hat x(k) = \sum_{n=0}^{N-1} x(n) \exp(-i 2 \pi k n / N)$.
Suppose you want $N$ samples of $\hat x(k)$. Then you would sample $x(t)$ exactly $N$ times, and you would get $N$ samples of $x(n)$ that you
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