8 Convolution Uses Flashcards
Identify: The delta function is seen as…
The delta function is seen as the identity for convolution. Convolving a signal with the delta function leaves the signal unchanged. This is the goal of systems that transmit or store signals.
Identify: The Delta function?
The delta function is the identity for convolution. Any signal convoluted with a delta function is left unchnaged
Identify Equation?
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Identify Graph?
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Uses: Amplification & Attentuation
Increasing or decreasing the amplitude of the delta function forms an impulse response that amplifies or attenuates respectively. (Amplifies signals by 1.6)
Amplification & Attenuation function description?
A system that amplifies or attenuates has scaled delta function for an impulse response. In this equation, k determines the amplification or attenuation
Amplification & Attenuation Function?
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Amplification & Attenuation Graph?
Here the impulse response will amplify the signal by 1.6
Uses Shift?
Shifting the delta function produces a corresponding shift between the input and output signals. Depending on the direction, this can be called a delay or an advance. This impulse response delays the signal by four samples
Uses: Shift Function description?
A relative shift between the input and the output signals corresponds to an impulse responce that is a shifted delta function. The variable, s determines the amount of shift in this equation.
Shift function?
Shift Graph?
Here the impulse response has been delayed by 4.
Applications for convolution in a low pass filter (Inverting Attenuator)?
Input signal * Impulse Response = Output signal
Applications for convolution, Low pass filters (Discrete Dereivative)?
Applications of Convolution - Low Pass filter?
Applications of convolution High-pass Filter?
Example convoluted signals from discrete to continuous?
x(n)=[1 1 1 1 1 1]
h(n)=[1 1 0 0 1 1]
y = conv (x , h) = [1 2 2 2 3 4 3 2 2 2 1]
