Podcast
Questions and Answers
A digital filter's frequency response describes how the filter affects signals at different frequencies. Which of these options directly relates to this response?
A digital filter's frequency response describes how the filter affects signals at different frequencies. Which of these options directly relates to this response?
- The magnitude and phase of the filter's output for different input frequencies. (correct)
- The order of the filter, indicating the number of poles and zeros.
- The locations of the poles and zeros in the complex plane.
- The coefficients of the difference equation.
When converting the system representation of a digital filter from its difference equation to its transfer function, what is the main transformation involved?
When converting the system representation of a digital filter from its difference equation to its transfer function, what is the main transformation involved?
- Expressing the filter's input-output relationship in the z-domain. (correct)
- Solving for the output signal in terms of the input signal and filter coefficients.
- Taking the Laplace transform of the difference equation.
- Analyzing the filter's behavior in the frequency domain.
A digital filter with a pole-zero diagram showing a pole close to the unit circle indicates which characteristic of the filter?
A digital filter with a pole-zero diagram showing a pole close to the unit circle indicates which characteristic of the filter?
- Strong attenuation of signals near the pole's frequency.
- Stable operation over a wide frequency range.
- Sharp transition between passband and stopband.
- High gain at specific frequencies. (correct)
For a given digital filter specification, such as a desired passband ripple and stopband attenuation, which system representation is most directly suited to determining the corresponding filter design parameters?
For a given digital filter specification, such as a desired passband ripple and stopband attenuation, which system representation is most directly suited to determining the corresponding filter design parameters?
When calculating the Fourier transform of a signal with a limited number of samples, how is the signal treated in terms of the frequency domain?
When calculating the Fourier transform of a signal with a limited number of samples, how is the signal treated in terms of the frequency domain?
Flashcards
Fourier Series
Fourier Series
A way to represent a periodic signal as a sum of sine and cosine functions.
Fourier Transform
Fourier Transform
Transforms a time-domain signal into its frequency-domain representation.
Digital Filter Representations
Digital Filter Representations
Different forms to describe a digital filter: pole-zero diagram, frequency response, etc.
Transfer Function
Transfer Function
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Difference Equation
Difference Equation
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Study Notes
Learning Goals
- Calculate the Fourier series for a signal with a limited period or the Fourier transform for a signal with a limited number of samples.
- Convert between different system representations for a digital filter (pole-zero diagrams, frequency response, transfer functions, difference equations, block diagrams).
- Understand the relationship between the specifications of a digital filter and the system representations.
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