Why Is Circular Convolution Important in Signal Processing?

AI Thread Summary
Circular convolution is an operation that wraps indices to keep them within a finite range, contrasting with linear convolution, which does not impose such limits. While linear convolution is generally preferred in signal processing, circular convolution is essential due to its computational efficiency, particularly in the frequency domain using the Fast Fourier Transform (FFT). The necessity of circular convolution arises from finite-length Discrete Fourier Transform (DFT) operations, which can introduce spectral artifacts. Understanding and mitigating the effects of circular convolution is crucial for effective signal processing, especially in applications involving windowing and filtering. Overall, circular convolution plays a significant role in optimizing signal processing techniques.
dexterdev
Messages
194
Reaction score
1
Hi PF,
What is circular convolution? Why do we need such an operation if we have linear convolution, What is its basic difference of both convolutions. Is circular convolution used only in frequency domain?

-Devanand T
 
Engineering news on Phys.org
http://ocw.mit.edu/resources/res-6-008-digital-signal-processing-spring-2011/study-materials/MITRES_6_008S11_lec10.pdf

According to these notes, we usually want linear convolution. But there's a fast algorithm for circular convolution, so we adapt that to do linear convolution.
 
that's a good pdf.

one note about meaning:

((n))_N \ \triangleq \ n\,\bmod\,N \ = \ n - N \left\lfloor \frac{n}{N} \right\rfloor

this just makes the index n wrap around so that it is always 0 \le n < N . that's what makes it circular.
 
Last edited:
I would offer that we don't particularly want circular convolution, but it is a necessary by-product of the finite-length DFT operations.

Circular convolution also drives the need for windowing and filtering to remove all of the translated spectral images. Learning to mitigate the negative effects of circular convolution is important.
 
Very basic question. Consider a 3-terminal device with terminals say A,B,C. Kirchhoff Current Law (KCL) and Kirchhoff Voltage Law (KVL) establish two relationships between the 3 currents entering the terminals and the 3 terminal's voltage pairs respectively. So we have 2 equations in 6 unknowns. To proceed further we need two more (independent) equations in order to solve the circuit the 3-terminal device is connected to (basically one treats such a device as an unbalanced two-port...
suppose you have two capacitors with a 0.1 Farad value and 12 VDC rating. label these as A and B. label the terminals of each as 1 and 2. you also have a voltmeter with a 40 volt linear range for DC. you also have a 9 volt DC power supply fed by mains. you charge each capacitor to 9 volts with terminal 1 being - (negative) and terminal 2 being + (positive). you connect the voltmeter to terminal A2 and to terminal B1. does it read any voltage? can - of one capacitor discharge + of the...
Thread 'Weird near-field phenomenon I get in my EM simulation'
I recently made a basic simulation of wire antennas and I am not sure if the near field in my simulation is modeled correctly. One of the things that worry me is the fact that sometimes I see in my simulation "movements" in the near field that seems to be faster than the speed of wave propagation I defined (the speed of light in the simulation). Specifically I see "nodes" of low amplitude in the E field that are quickly "emitted" from the antenna and then slow down as they approach the far...

Similar threads

Back
Top