3. Sampling, Reconstruction, and Aliasing: Time and Frequency Domains
Sampling, reconstruction, and aliasing are crucial concepts in signal processing that bridge continuous and discrete time signals, highlighting the importance of time and frequency domains. The chapter addresses the implications of sampling rates on signal accuracy and the potential for distortion through aliasing. Additionally, methods such as Fourier analysis and Short-Time Fourier Transform (STFT) are discussed, emphasizing their roles in analyzing signals over time and frequency.
Sections
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What we have learnt
- Sampling converts continuous-time signals into discrete-time signals at specific intervals.
- Aliasing occurs when the sampling rate is insufficient to capture high-frequency components, causing distortions.
- The Nyquist frequency is critical in determining the appropriate sampling rate to avoid aliasing.
Key Concepts
- -- Sampling
- The process of converting a continuous-time signal into a discrete-time signal by measuring it at specific intervals.
- -- Aliasing
- A phenomenon where high-frequency components of a signal become indistinguishable from lower frequencies due to insufficient sampling.
- -- Nyquist Frequency
- Half of the sampling rate; it determines the maximum frequency that can be accurately represented without aliasing.
- -- Fourier Transform
- A mathematical transform that converts a time-domain signal into its frequency-domain representation.
- -- ShortTime Fourier Transform (STFT)
- A variation of the Fourier Transform that analyzes the frequency content of a signal over short time segments.
Additional Learning Materials
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