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Questions and Answers
What consequence occurs if an analog signal is not appropriately sampled?
What consequence occurs if an analog signal is not appropriately sampled?
According to the sampling theorem, what is the minimum sampling rate needed to sample a signal with a maximum frequency component of 10 kHz?
According to the sampling theorem, what is the minimum sampling rate needed to sample a signal with a maximum frequency component of 10 kHz?
If a speech signal contains frequencies up to 4 kHz, what must be the sampling frequency to avoid aliasing?
If a speech signal contains frequencies up to 4 kHz, what must be the sampling frequency to avoid aliasing?
Which of the following statements about the sampling theorem is NOT true?
Which of the following statements about the sampling theorem is NOT true?
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For a signal sampled at a rate of 100 Hz, what is the maximum frequency component that can theoretically be accurately represented without aliasing?
For a signal sampled at a rate of 100 Hz, what is the maximum frequency component that can theoretically be accurately represented without aliasing?
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What is a characteristic of continuous-time signals?
What is a characteristic of continuous-time signals?
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Which representation method is NOT typically used for discrete-time signals?
Which representation method is NOT typically used for discrete-time signals?
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What does the amplitude 'A' represent in the equation x(t) = Asin(2π f t + ϕ)?
What does the amplitude 'A' represent in the equation x(t) = Asin(2π f t + ϕ)?
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Which of the following is a feature of discrete-time signals?
Which of the following is a feature of discrete-time signals?
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In time-domain representation, what does the frequency 'f' indicate?
In time-domain representation, what does the frequency 'f' indicate?
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Which of the following best describes the time domain?
Which of the following best describes the time domain?
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What is represented by the variable 'ϕ' in the time-domain signal equation?
What is represented by the variable 'ϕ' in the time-domain signal equation?
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What type of signal is represented by the equation x[n] = sin(2π f nT)?
What type of signal is represented by the equation x[n] = sin(2π f nT)?
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What does the frequency domain represent in relation to a signal?
What does the frequency domain represent in relation to a signal?
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Which function represents the signal in the frequency domain?
Which function represents the signal in the frequency domain?
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What process does the ADC use to convert an analog signal into a digital signal?
What process does the ADC use to convert an analog signal into a digital signal?
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What is defined as the time span between two sample points in a digital signal processing context?
What is defined as the time span between two sample points in a digital signal processing context?
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When sampling an analog signal, what is the role of the sample and hold process?
When sampling an analog signal, what is the role of the sample and hold process?
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What is the minimum sampling rate needed to ensure accurate reconstruction of an analog signal?
What is the minimum sampling rate needed to ensure accurate reconstruction of an analog signal?
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If the sampling period is T = 125 microseconds, what is the corresponding sampling rate in samples per second?
If the sampling period is T = 125 microseconds, what is the corresponding sampling rate in samples per second?
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What issue arises from digitizing an infinite number of points of an analog signal?
What issue arises from digitizing an infinite number of points of an analog signal?
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Study Notes
Digital Signal Processing (DSP) Lecture 2 Notes
- A signal is a function conveying information about a phenomenon's behavior or attributes.
- Signals can be continuous or discrete.
- Continuous-time signals are defined for every value of time (t).
- Example: x(t) = sin(2πft), where t is a continuous variable.
- Discrete-time signals are defined only at discrete points in time.
- Example: x[n] = sin(2πfnT), where n is an integer, and T is the sampling period.
Representation of Discrete-Time Signals
- Discrete-time signals are defined only at discrete time instants.
- The amplitude between two time instants isn't defined.
- Discrete-time signals are represented by x(n).
- Four ways to represent discrete-time signals:
- Graphical representation
- Functional representation
- Tabular representation
- Sequence representation
Graphical Representation
- Example: Given x(-2) = -3, x(-1) = 2, x(0) = 0, x(1) = 3, x(2) = 1, and x(3) = 2.
- The signal can be graphed with discrete points on a number line with n as the independent variable (horizontal axis) and x(n) as the dependent variable (vertical axis).
Functional Representation
-
Represented as an equation.
-
Example: x(n) = { -3, n= -2 { 2, n= -1 { 0, n= 0 { 3, n= 1 { 1, n= 2 { 2, n= 3
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Or in alternative form: x(n) = 2nu(n)
Tabular Representation
- Discrete-time signals represented as a table
- Example: | n | x(n) | |---|---| | 2 | 3 | | 1 | 2 | | 0 | 0 | | 1 | 3 | | 2 | 1 | | 3 | 2 |
Sequence Representation
- A list within curly brackets
- Example: x(n) = {-3, 2, 0, 3, 1, 2}
Time and Frequency Domains
-
Time Domain: Represents a signal as it varies over time (graphically or functionally).
- Useful for observing how signals change and for audio signals and sensor readings.
- Frequency Domain: Represents a signal in terms of its frequency components (spectrum). Identifies the frequency content within ranges.
- signals like sound or sensor readings
- Example: Given signal x(t) == Asin(2𝝿ft + 𝝋) ,
- A = Amplitude.
- f = Frequency.
- 𝝋 = Phase shift
ADC Unit
- Samples analog signal.
- Quantizes sampled signal.
- Encodes quantized levels to a digital signal.
Sampling of Continuous Signals
- An analog signal (continuous time) is represented on a graph where every point has a value.
- Digitizing an infinite number of points is computationally hard.
- Sampling takes discrete points from the signal (with fixed interval T).
Sampling Theorem
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An analog signal can be perfectly reconstructed from its samples fs (sampling rate) at least twice the maximum frequency (max frequency= fmax) in the signal.
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fs ≥ 2 * fmax
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For example:
- Speech signal with max frequency of 4 kHz needs sampling rate of at least 8 kHz.
- Audio signal with max frequency of 20 kHz needs sampling rate of at least 40 kHz.
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Description
This quiz explores key concepts of the sampling theorem and its implications for signal processing. Questions cover minimum sampling rates, characteristics of signals, and potential consequences of improper sampling. Test your understanding of how frequency components are represented in both continuous and discrete-time signals.
