Efficient Computation of Convolution using Z-Transform in Discrete-Time Signals

[cutesteph]

x_1(n) = (!/4)^n u(n-1) and x_2(n) = [1- (1/2)^n] u(n)

X_1(z) = (1/4)z^-1 / (1-(!/4)z^-1 and X_2(z) = 1/(1-z^-1) + 1/(1-(1/2)z^-1)

Y(z) = X_1(z) X_2(z) = (-4/3) /(1-(1/4)z^-1 + (1/3) / (1-z^-1) + 1/(1-(1/2)z^-1

 

[rbj]

may i suggest that you try using the \LaTeX pasteup provided by physicsforums? it makes it much easier to read. also try to use the convention of square brackets (instead of parenths) for discrete-time or discrete-frequency signals. like

x[n] = \frac{1}{N} \sum_{k=0}^{N-1} X[k] e^{j 2 \pi k n / N}

as opposed to

x(t) = \int_{-\infty}^{+\infty} X(f) e^{j 2 \pi f t} df

z is a continuous variable, BTW. but n is discrete.