# Convolution of Two Discrete Signals with Non-Zero Impulse Response

• fifodido
In summary, a discrete signal is a type of signal that is represented by a sequence of discrete, distinct values, and is typically used in digital systems. It is different from a continuous signal, which has an infinite number of possible values. A discrete signal is also different from a digital signal, which only has two possible values (0 and 1). Two discrete signals can have different sampling rates, and they are commonly used in data analysis to represent and analyze digital data.
fifodido
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

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.

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]

## 1. What is a discrete signal?

A discrete signal is a type of signal that is represented by a sequence of discrete, distinct values. These values are typically sampled at regular intervals and are often used to represent continuous, analog signals in digital systems.

## 2. How is a discrete signal different from a continuous signal?

A discrete signal is different from a continuous signal in that it is made up of a series of distinct values, while a continuous signal has an infinite number of possible values. Discrete signals are typically used in digital systems, while continuous signals are used in analog systems.

## 3. What is the difference between a discrete signal and a digital signal?

A discrete signal is a type of signal that is represented by a sequence of discrete, distinct values, while a digital signal is a discrete signal that only has two possible values (0 and 1). In other words, all digital signals are discrete signals, but not all discrete signals are digital signals.

## 4. Can two discrete signals have different sampling rates?

Yes, two discrete signals can have different sampling rates. The sampling rate refers to the frequency at which the values of a discrete signal are recorded. Different sampling rates can affect the accuracy and quality of the signal, so it is important to consider when working with multiple discrete signals.

## 5. How are discrete signals used in data analysis?

Discrete signals are commonly used in data analysis to represent and analyze digital data. This can include analyzing digital images, audio recordings, or other types of digital data. Discrete signals can also be used in signal processing and filtering techniques to extract useful information from the data.

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