(Solved): An LTI system is described by the difference equation y[n]=x[n]-2x[n-1] x[n-2]. Its output signal y[ ...
An LTI system is described by the difference equation
y[n]=x[n]-2x[n-1] x[n-2]. Its output signal
y[n]approximates computation of the second derivative of the input signal
x[n]. i) Calculate and sketch the system impulse response
h[n](recall that
h[n]=y[n]when
x[n]=\delta [n]). Is this a causal system? Is it (BIBO) stable? State reasons for your answers. ii) Consider the input signal
x[n]=[1,4,9](in this vector representation of
x[n], the underlined sample is the sample at time index
n=0; sample values at other time indices not listed have zero values). Calculate the output
y[n]=x[n]^(**)h[n]over
-1<=n<=6, where ***denotes linear convolution. Use a tabular approach to evaluate the convolution. Over what time indices
nis the output
y[n]neither transient nor end effect? Briefly explain, iii) Compute
y[n]=h[n]^(**)x[n]numerically using the Matlab function 'conv' and check your answer to part (ii) above. Is the length of
y[n]as expected? Explain. [Hint: type "help conv" in the Matlab command window to learn more about the input and output arguments of the "conv" function].
