List of useful Transforms
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Pointwise product of two function in continuous time domain → Linear convolution in frequency domain
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Pointwise product of two functions in the continuous (Fourier) frequency domain → Linear convolution in the time domain
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Elementwise product of two vectors in the time domain → Circular convolution in the discrete (DFT) frequency domain
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Elementwise product of two vectors in the discrete (DFT) frequency domain → Circular convolution in the time domain
DFT properties
- Shifting property - similar to that in continuous Fourier Transform \( z_k = x_k \exp{j\pi k } \)
OFDM implementation
OFDM transmitter:
- Encode the incoming bytes with added redundancy for error correction in DFT domain by
Channel estimation and synchronization
Channel estimation with random OFDM symbols:
Following methods can be used for synchronization:
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Chirp
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Schmidl & Cox synchronization
