Convolution of Two Discrete Signals with Non-Zero Impulse Response

[fifodido]

please help me in this problem:
two discrete signals
x[nT]={0 0 1 0 0 2 2 2 2}
h[nT]=[-1 2 3 3 2 1]


find there convolution if the impulse response doesn't start from zero
,use the table or the matrix

 

[wildman]

Go to the net and find a free book: "Digital Signal Processing" by Steven Smith. Then go to chapter 6. That chapter includes a step by step discription of what you have to do. If you have more question after reading that, then ask.

 

[piercas]

The convolution of two discrete signals with non-zero impulse response is a mathematical operation that combines the two signals to produce a third signal. In this case, we have two signals x[nT] and h[nT], with the impulse response h[nT] starting at a non-zero value. To find the convolution of these two signals, we can use the convolution sum formula:

y[nT] = ∑x[kT]h[(n-k)T]

where k is the index of the summation and n is the index of the output signal.

To simplify the process, we can use a table or a matrix to calculate the convolution. In the table, we can write the values of the two signals and the impulse response, and then perform the multiplication and addition operations to find the resulting signal. In the matrix method, we can represent the signals and the impulse response as vectors and use matrix multiplication to find the convolution.

Using either method, we can find the convolution of x[nT] and h[nT] as follows:

y[0T] = x[0T]h[0T] = 0*[-1] = 0
y[T] = x[0T]h[T] + x[T]h[0T] = 0*2 + 0*[-1] = 0
y[2T] = x[0T]h[2T] + x[T]h[T] + x[2T]h[0T] = 0*3 + 0*2 + 1*[-1] = -1
y[3T] = x[0T]h[3T] + x[T]h[2T] + x[2T]h[T] + x[3T]h[0T] = 0*3 + 0*3 + 1*2 + 0*[-1] = 2
y[4T] = x[0T]h[4T] + x[T]h[3T] + x[2T]h[2T] + x[3T]h[T] + x[4T]h[0T] = 0*2 + 0*3 + 1*3 + 0*2 + 0*[-1] = 3
y[5T] = x[0T]