The Convolution Sum The output of an LTI system is the convolution sum of the input to the system and the impulse response of the system. yIn]=xn]*hin]=>xk]hin-k] k=-00 Derivation:8[n]->h[n](impulse response) 6[n-k]->h[n-k](time invariance) x[k]8[n-k]>x[k]h[n-k](homogeneity) x[n]=∑x[k]n-k]→y[n=∑x[k]Mn-] k=-00 r=-c (superposition)The Convolution Sum • The output of an LTI system is the convolution sum of the input to the system and the impulse response of the system. [ ] [ ]* [ ] [ ] [ ] Derivation: [ ] [ ] (impulse response) [ ] [ ] (time invariance) [ ] [ ] [ ] [ ] (homogeneity) [ ] [ ] [ ] [ ] [ ] [ ] (superposition) k k k y n x n h n x k h n k n h n n k h n k x k n k x k h n k x n x k n k y n x k h n k                            