EE5410 Signal Processing --impulse response h[n] and convolutions

EE5410 Signal Processing --impulse response h[n] and convolutions
曉 -- 宇智波鼬的寫輪眼

1. When the input to the FIR filter is a unit impulse sequence, x[n] = delta[n], the output is, by definition, the unit impulse response h[n].

2. The impulse response h[n] of the FIR filter is simply the sequence of difference equation coefficients. Since h[n]=0 for n < 0 and for n >M, the length of the impulse response sequence h[n] is finite.

3. When the relation between the input and the output of the FIR filter is expressed in terms of the input and the impulse response h[n], it is called a finite convolution sum, and we say that the out is obtained by convolving the sequences x[n] and h[n].

4. The impulse response h[n] of the LTI system is simply the output when the input isthe unit impulse sequence delta[n].

5. The impulse response h[n] is a complete characteization for ANY LTI system, and that convolution is the general formula that allows us to compute the output from the input for ANY LTI system.

6. ANY signal x[n] can be represented as a sum of SCALED and SHIFTED impulse signals.

曉 -- 宇智波鼬的寫輪眼
http://www.youtube.com/watch?v=fG4O71A6kvw&feature=related

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