Convolution is used to find:a)The impulse response of an LTI Systemb)F...
Explanation: Convolution is the combination of addition and multiplication of the signals and used to find the impulse response of the LTI system.
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Convolution is used to find:a)The impulse response of an LTI Systemb)F...
Convolution is a fundamental mathematical operation used in various fields, including signal processing and system analysis. It involves combining two functions to produce a third function that represents the interaction between them. In the context of an LTI (Linear Time-Invariant) system, convolution is used to find the time response of the system.
1. Definition of Convolution:
Convolution is a mathematical operation that combines two functions, let's say f(t) and h(t), to produce a new function, which we'll denote as g(t). The convolution of f(t) and h(t) is denoted as g(t) = f(t) * h(t) and is defined as follows:
g(t) = ∫[f(τ) * h(t-τ)]dτ
2. Impulse Response of an LTI System:
The impulse response of an LTI system is the output of the system when an impulse function, usually denoted as δ(t), is applied as the input. By convolving the impulse function with the system's transfer function, we obtain the impulse response. Therefore, option 'A' is incorrect.
3. Frequency Response of a System:
The frequency response of a system is the relationship between the input and output signals in the frequency domain. It is typically obtained by applying a sinusoidal input signal at different frequencies to the system and analyzing the corresponding output. While convolution is involved in the process of calculating the frequency response, it is not used directly to find it. Therefore, option 'B' is incorrect.
4. Time Response of an LTI System:
The time response of an LTI system refers to how the system behaves over time when a specific input signal is applied. It is obtained by convolving the input signal with the impulse response of the system. The impulse response represents the system's behavior to a unit impulse, and by convolving it with the input signal, we can determine the system's output over time. Therefore, option 'C' is the correct answer.
5. Phase Response of an LTI System:
The phase response of an LTI system represents the phase shift experienced by the input signal at different frequencies when it passes through the system. While convolution is involved in the process of calculating the phase response, it is not used directly to find it. Therefore, option 'D' is incorrect.
In summary, convolution is primarily used to find the time response of an LTI system by convolving the input signal with the system's impulse response. It is a fundamental operation in system analysis and is not directly used to find the impulse response, frequency response, or phase response of a system.
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