Final answer:
The subject of the question is discrete time convolution, a process in engineering that combines two sequences to determine the output of a linear time-invariant system. It involves flipping, shifting, multiplying, and summing the impulse response function and the input signal.
Step-by-step explanation:
The question is asking about the process of discrete time convolution, which is a fundamental concept in the field of signals and systems within engineering. Discrete time convolution is a mathematical operation that combines two sequences to produce a third sequence, representing the amount of overlap between the sequences as they are shifted past each other. This operation is critical for understanding the output of a linear time-invariant system when given an input signal. The process requires you to flip one sequence (the impulse response), shift it, multiply it by the other sequence (the input signal), and sum the results to obtain the output sequence.
To perform a discrete time convolution, you follow these steps:
- Flip the impulse response function, h[n], to get h[-n].
- Shift h[-n] by an integer number of samples, producing h[n-k], for each value of k.
- Multiply the shifted impulse response with the input signal, x[n], for each value of n, resulting in x[n] * h[n-k].
- Sum the products over all values of n to find the value of the output signal, y[k], at the current shift k.
- Repeat this process for all values of k to obtain the full convolution result.
The impulse response function and the input signal must be defined in order to apply this process and find the convolution sum which will give us the response of the system to the given input.