FIR filters, impulse responses and unit step function

In summary, a Finite Impulse Response (FIR) filter is a type of digital filter that uses a finite number of past input samples to calculate the current output value. It has a finite impulse response, meaning that its output will eventually settle to zero after a finite number of input samples. The impulse response of a system is the output that results when a unit impulse signal is applied to the input of the system. A unit step function is a mathematical function that is defined as 0 for negative inputs and 1 for positive inputs, often used to model events with a sudden change. The main difference between FIR filters and Infinite Impulse Response (IIR) filters is that IIR filters have feedback, resulting in a more complex frequency response
  • #1
Jd303
35
0
Hey everyone, the question I am faced with is this:

Which of the following expressions involving δ[n] is incorrect?
where "m" is a non zero integer and u[n] is the unit step function.

A. u[n-m] = δ[n] + u[n-m+1]

B. x[n]δ[n-m] = x[n-m]

C. δ[n] = u[n] - u[n-1]

D. δ[n]δ[n-m] = 0

I have been scratching my head for a while, but really not sure what to do. Any help as always would be greatly appreciated!
 
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  • #2
Hey Jd, take a shot at each of these, explain your rationale & then maybe we can be of help.
 

What is a FIR filter?

A Finite Impulse Response (FIR) filter is a type of digital filter used in signal processing that utilizes a finite number of past input samples to calculate the current output value. It has a finite impulse response, meaning that its output will eventually settle to zero after a finite number of input samples.

What is an impulse response?

The impulse response of a system is the output that results when a unit impulse signal is applied to the input of the system. In other words, it shows how a system responds to a sudden, short burst of energy. In the context of FIR filters, the impulse response is the filter's output when the input is a unit impulse function.

What is a unit step function?

A unit step function, also known as a Heaviside function, is a mathematical function that is defined as 0 for negative inputs and 1 for positive inputs. It represents a sudden change from 0 to 1 at a specific point, and is often used to model events that have a "start" but no "duration". In the context of FIR filters, the unit step function is often used as an input signal to test the filter's behavior.

What is the difference between a FIR filter and an IIR filter?

The main difference between FIR filters and Infinite Impulse Response (IIR) filters is that IIR filters have feedback in their calculation equations, meaning that the output is dependent on both current and past inputs. This can result in a more complex frequency response, whereas FIR filters have a simpler frequency response since they only depend on past inputs.

What is the purpose of a FIR filter?

FIR filters are often used for tasks such as noise reduction, signal smoothing, and frequency selection. They are also commonly used in digital signal processing applications, as they can be easily implemented in software. FIR filters can also be designed to have linear phase response, meaning that all frequencies in the input signal experience the same delay, making them useful for applications such as audio equalization.

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