Minia University Faculty of Engineering

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Electrical Engineering Department DSP for 4^th Year electronic and communication

Minia University Faculty of Engineering

Digital Signal Processing

Tel: 01284240601 E-mail: [email protected]

Lecture 6

Dr / Gerges Mansour

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Lecture 6 Dr. Eng. Gerges M. Salama

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DSP

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DSP

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DSP

❑ The algorithm transforming the time domain signal samples to the frequency domain components is known as the discrete Fourier transform, or DFT.

❑ The DFT also establishes a relationship between the time domain representation and the frequency domain representation. Therefore, we can apply the DFT to perform frequency analysis of a time domain sequence.

❑ The DFT is widely used in many other areas, including spectral analysis,

acoustics, imaging/video, audio, instrumentation, and communications

systems.

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DSP

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DSP

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DSP

We refer 𝐶 _𝑘 as discrete-time Fourier series coefficients. Since the coefficients

𝐶 _𝑘 are obtained from the Fourier series expansion in the complex form, the

resultant spectrum 𝐶 _𝑘 will have two sides.

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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DSP

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Minia University Faculty of Engineering

Minia University Faculty of Engineering

Digital Signal Processing

Lecture 6

Dr / Gerges Mansour

DSP

DSP

DSP

❑ The algorithm transforming the time domain signal samples to the frequency domain components is known as the discrete Fourier transform, or DFT.

❑ The DFT also establishes a relationship between the time domain representation and the frequency domain representation. Therefore, we can apply the DFT to perform frequency analysis of a time domain sequence.

❑ The DFT is widely used in many other areas, including spectral analysis,

acoustics, imaging/video, audio, instrumentation, and communications

systems.

DSP

DSP

DSP

We refer 𝐶 𝑘 as discrete-time Fourier series coefficients. Since the coefficients

𝐶 𝑘 are obtained from the Fourier series expansion in the complex form, the

resultant spectrum 𝐶 𝑘 will have two sides.

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

DSP

We refer 𝐶 _𝑘 as discrete-time Fourier series coefficients. Since the coefficients

𝐶 _𝑘 are obtained from the Fourier series expansion in the complex form, the

resultant spectrum 𝐶 _𝑘 will have two sides.