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### Table of Contents:

- What is the purpose of a notch filter?
- What are the basic elements of DSP?
- What are the applications of DSP?
- What is the need for FFT algorithm?
- How do you calculate twiddle factor?
- What is linear and circular convolution in DSP?
- What is convolution and give its application?
- Why do we need circular convolution?
- Is linear convolution better or circular convolution Why?
- Why do we use convolution?
- Is a convolution linear?
- What is meant by circular convolution in DSP?
- What is DFT and its properties?
- What is the DFT of the four point sequence?
- What is the difference between convolution and correlation?
- What are the types of convolution?
- Can we perform correlation using convolution?
- Why is correlation not commutative?
- How do you know if two signals are similar?
- What is the difference between cross correlation and auto correlation?
- What does cross correlation mean?

## What is the purpose of a notch filter?

A **notch filter**, usually a simple LC circuit, is used to remove a specific interfering frequency. This is a technique used with radio receivers that are so close to a transmitter that it swamps all other signals. The wave trap is used to remove or greatly reduce the signal from the nearby transmitter.

## What are the basic elements of DSP?

**A DSP contains these key components:**

- Program Memory: Stores the programs the
**DSP**will use to process data. - Data Memory: Stores the information to be processed.
- Compute Engine: Performs the math processing, accessing the program from the Program Memory and the data from the Data Memory.

## What are the applications of DSP?

DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for **telecommunications**, control systems, ...

## What is the need for FFT algorithm?

As the name implies, the **Fast Fourier Transform** (**FFT**) is an **algorithm** that determines Discrete Fourier Transform of an input significantly faster than computing it directly. In computer science lingo, the **FFT** reduces the number of computations needed for a problem of size N from O(N^2) to O(NlogN) .

## How do you calculate twiddle factor?

**Twiddle factors** (represented with the letter W) are a set of values that is used to speed up DFT and IDFT calculations. For a discrete sequence x(n), we can **calculate** its Discrete Fourier Transform and Inverse Discrete Fourier Transform using the following equations.

## What is linear and circular convolution in DSP?

**Linear convolution** is the basic operation to calculate the output for any **linear** time invariant system given its input and its impulse response. **Circular convolution** is the same thing but considering that the support of the signal is periodic (as in a circle, hance the name).

## What is convolution and give its application?

The term **convolution** refers to both the result function and to the process of computing it. ... **Convolution** has **applications** that include probability, statistics, acoustics, spectroscopy, signal processing and image processing, engineering, physics, computer vision and differential equations.

## Why do we need circular convolution?

"**Circular convolution** is used to convolve two discrete Fourier transform (DFT) sequences." MATLAB documentation says this. To me, **circular convolution** is an operation on any sequences. ... Also, **circular convolution** is defined for 2 sequences of equal length and the output also would be of the same length.

## Is linear convolution better or circular convolution Why?

Here y(n) is a periodic output, x(n) is a periodic input, and h(n) is the periodic impulse response of the LTI system. In **linear convolution**, both the sequences (input and impulse response) may or may not be of equal sizes. ... Thus the output of a **circular convolution** has the same number of samples as the two inputs.

## Why do we use convolution?

**Convolution** is a mathematical way of combining two signals to form a third signal. It is the single most important technique in Digital Signal Processing. ... **Convolution** is important because it relates the three signals of interest: the input signal, the output signal, and the impulse response.

## Is a convolution linear?

, **Convolution** is a **linear** operator and, therefore, has a number of important properties including the commutative, associative, and distributive properties.

## What is meant by circular convolution in DSP?

**Circular convolution**, also known as **cyclic convolution**, is a special case of periodic **convolution**, which is the **convolution** of two periodic functions that have the same period. Periodic **convolution** arises, for example, in the context of the discrete-time Fourier transform (DTFT).

## What is DFT and its properties?

The **DFT** has a number of important **properties** relating time and frequency, including shift, circular convolution, multiplication, time-reversal and conjugation **properties**, as well as Parseval's theorem equating time and frequency energy.

## What is the DFT of the four point sequence?

We know that **the 4**-**point DFT** of the above given **sequence** is given by the expression. X(k)=\sum_{n=0}^{N-1}x(n)e^{-j2πkn/N} In this case N=4. =>X(0)=6,X(1)=-2+2j,X(2)=-2,X(3)=-2-2j. 10.

## What is the difference between convolution and correlation?

Theoretically, **convolution** are linear operations on the signal or signal modifiers, whereas **correlation** is a measure of similarity **between** two signals. As you rightly mentioned, the basic **difference between convolution and correlation** is that the **convolution** process rotates the matrix by 180 degrees.

## What are the types of convolution?

**Convolution** Arithmetic. Transposed **Convolution** (Deconvolution, checkerboard artifacts) Dilated **Convolution** (Atrous **Convolution**) Separable **Convolution** (Spatially Separable **Convolution**, Depthwise **Convolution**)

## Can we perform correlation using convolution?

**Convolution** is identical to **correlation** except that the kernel is flipped before **correlation**. **Convolution** is only a measure of similarity between two signals if the kernel is symmetric, making the problem equivalent to **correlation**.

## Why is correlation not commutative?

Cross **correlation** is **not commutative** like convolution i.e. If R12(0) = 0 means, if ∫∞−∞x1(t)x∗2(t)dt=0, then the two signals are said to be orthogonal. ... Cross **correlation** function corresponds to the multiplication of spectrums of one signal to the complex conjugate of spectrum of another signal.

## How do you know if two signals are similar?

Similarity in energy (or power **if different** lengths): Square **the two signals** and sum each (and divide by **signal** length **for** power). (Since **the signals** were detrended, this should be **signal** variance.) Then subtract and take absolute value **for** a measure of **signal** variance similarity.

## What is the difference between cross correlation and auto correlation?

**Cross correlation** happens when two different sequences are **correlated**. **Autocorrelation** is the **correlation between** two of the same sequences. In other words, you **correlate** a signal with itself.

## What does cross correlation mean?

multiple time series

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