Understanding Linear Convolution

What is the main property of linear convolution in signal processing? A) The output signal has a higher frequency than the input signal. B) The output is the sum of the two input signals. C) The output is the weighted sum of past values of the two signals. D) The output is the difference between the two signals.

• C) The output is the weighted sum of past values of the two signals.

• The output is a constant value regardless of the inputs.

• The output is the product of the two input signals.

• The output is a time-shifted version of the input signals.

Which of the following best describes the process of linear convolution? A) The result is obtained by multiplying the signals element-wise. B) The result is obtained by shifting, multiplying, and summing the signals. C) The result is obtained by adding the signals element-wise. D) The result is obtained by performing a Fourier transform.

• The result is obtained by convolving the signals in the frequency domain.

• The result is obtained by integrating the signals.

• The result is obtained by subtracting the signals element-wise.

• B) The result is obtained by shifting, multiplying, and summing the signals.

In linear convolution, if one of the signals is a delta function, what is the output? A) The output will be zero. B) The output will be a scaled version of the other signal. C) The output will be a constant signal. D) The output will be a random signal.

• The output will be a delayed version of the other signal.

• The output will be a periodic signal.

• B) The output will be a scaled version of the other signal.

• The output will be the same as the delta function.

What is the mathematical representation of linear convolution? A) x(t) * h(t) B) x(t) + h(t) C) x(t) - h(t) D) x(t) / h(t)

• x(t) - h(t)

• x(t) / h(t)

• x(t) + h(t)

• A) x(t) * h(t)

Which property of convolution states that the order of the signals does not affect the output? A) Commutative property B) Associative property C) Distributive property D) Identity property

• G) Reflexive property

• F) Linear property

• E) Inverse property

• A) Commutative property

In the context of linear convolution, what does the term 'kernel' refer to? A) The input signal B) The output signal C) The filter applied to the input signal D) The noise in the system

• C) The filter applied to the input signal

• E) The sampling rate of the signal

• F) The duration of the input signal

• G) The frequency response of the system

What is the effect of increasing the length of the input signal in linear convolution? A) The output length decreases B) The output length remains the same C) The output length increases D) The output becomes distorted

• A) The output length decreases

• B) The output length remains the same

• D) The output becomes distorted

• C) The output length increases

Which of the following is a common application of linear convolution? A) Image processing B) Data compression C) Encryption D) Network routing

• D) Image enhancement

• C) File archiving

• A) Image processing

• B) Video streaming

What is the relationship between linear convolution and the Fourier transform? A) They are unrelated B) Convolution in time domain corresponds to multiplication in frequency domain C) Convolution in time domain corresponds to addition in frequency domain D) They are the same operation

• Convolution in time domain has no effect on frequency domain

• Fourier transform is a type of convolution

• B) Convolution in time domain corresponds to multiplication in frequency domain

• Convolution in time domain corresponds to division in frequency domain

What is the output of convolving a signal with itself? A) The original signal B) A scaled version of the original signal C) A new signal with doubled duration D) A signal with increased frequency components

• A signal with reduced amplitude

• A signal with a different phase shift

• A signal that is the inverse of the original

• B) A scaled version of the original signal