One of DSP low-pass filter design experiment: Fourier transform

This is actually my DSP course design, frankly speaking, a semester of the DSP course did not make me on the DSP chip to increase how much understanding, more harvest is finally know before looking like the Heavenly Book Digital signal processing is used to do what, however, this also does not have any eggs, also did not reduce my hatred of Fourier, Haha, I'm joking.

Design a low-pass filter, which is actually a very simple and simple course design, even, also called the curriculum design, is not called the experiment too. I want to write it, one is near graduation, want to make some interesting things to share before, otherwise they can only lie quietly in the hard drive slowly forgotten, was deleted. Second, of course, for the benefit of all of you still "struggling" in the paradise of "students". Inserted a sentence, recently in the internship, only to find that the school is really the closest place to heaven, still in heaven, please cherish. In fact, I just want to let the younger brothers and sisters have a preliminary understanding of how the Fourier transform is applied in practice, and not just the back of a few unknown formula, I would like to back the frequency domain multiplication equivalent to the time domain convolution to test the signal and system .... , the first attempt to write something, not to blame.

First of all, the great God masterpiece http://zhuanlan.zhihu.com/wille/19763358, well, after reading still do not know to kill the author it, and I have nothing to do, bye ....

To be honest, if you see the masterpiece of the Great God earlier, you may not need to foggy the exam, in general, we have to use the Fourier transform, the general signal in the time domain is a number of different frequencies and amplitude of the sine wave synthesis, waveform clutter, we can not directly deal with it, And through the Fourier transform into the frequency domain can intuitively see the frequency of each sine wave, in the frequency domain of each frequency component processing, such as the deletion of a certain frequency, after the inverse Fourier transform will get the signal we want. To say, the time domain to the frequency domain, and then from the frequency domain to the time domain is only a process of understanding, not that in the DSP chip running program is the first Fourier transform, processing and then reverse transformation process. The frequency domain and the time domain are two different spaces, reflects the same object, in a space to deal with this object in another space will also see its changes, for example, the time domain and frequency domain is like a person's front and behind, in this person behind a slap, you see in front of the face is not a slap, right, What you see is this guy spit a mouthful of blood ... And the Fourier transform is the connection between this slap and the blood. This can be a good explanation of "frequency domain multiplication equivalent to the time domain convolution" This sentence, the time domain inside the convolution operation to go through the rollover, shift, multiplication, etc., but all of this in the frequency domain is only a multiplication operation.

Needless to say,, before or before the master works, http://www.cnblogs.com/BitArt/archive/2012/11/24/2786390.html, which refers to the digital signal processing of the first step, sampling, Sampling of the specific principles of deduction forgive me also can not tell, only to say that sampling in practice is often said that the mold/number conversion, is through a A/d chip to the analog signal into a series of digital DSP to deal with, in the yellow circle Live is the experiment with a/d chip TLC320AD50,

As mentioned earlier, Fourier indicates that any signal is composed of different frequencies and amplitude of the sine wave, the following to synthesize two different frequency sine wave signal, forgive me matlab temporary learning, preface use ....

As can be seen, the frequency domain diagram clearly shows that our signal only 1000Hz frequency components, similarly, a 4kHz sine wave signal is as follows,

It can be predicted that if the two frequency component of the sine wave signal synthesis, its frequency domain is what it looks like, as follows

That is, there are many interesting links between the time domain and the frequency domain, interested can be concerned about, basically, the Fourier transform is very powerful and useful, write this more is due to read the first blog post felt and write, so far from the online blog to benefit a lot, and sometimes do it yourself, although simple, But to see the expected result is still very happy.

One of DSP low-pass filter design experiment: Fourier transform