In this lesson you will learn when a continuous-time signal can be reconstructed from its samples and how to do the reconstruction. These insights are easy to obtain using the frequency domain representation for sampling that is derived in the preceding lesson. The condition for unique reconstruction is that the sampling theorem be satisfied. The […]
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Parks-McClellan FIR Filter Design
The minimax design method developed by Parks and McClellan is the most powerful method for FIR filter design. In this lesson you will learn the principles of the minimax optimal approach. You will also learn how a weighting function is used to specify the relative response error in the pass and stop bands of the […]
Circular Convolution Property of the Discrete Fourier Transform
The Circular Convolution Property of the Discrete Fourier Transform lesson takes a detailed look at the convolution-multiplication property for the DFT. You will learn how to derive this important property, how to evaluate circular convolution, and the relationship between linear or ordinary and circular convolution. Understanding these concepts is key for properly using the DFT […]
Difference Equations: Solving System Responses with Stored Energy
Difference equations are one of the few descriptions for linear time-invariant (LTI) systems that can incorporate the effects of stored energy - that is, describe systems which are not at rest when the input is applied. In this lesson you will learn how the output of a LTI system described by a difference equation can be expressed as […]
Properties of the Fourier Transform
In this lesson you will learn several of the most important Fourier transform properties and how to apply them. Understanding the properties of the Fourier transform will help you develop your insight regarding the relationships between time- and frequency-domain representations of signals. You will gain insight how specific manipulations of a signal in either the […]
Filtering with the Discrete Fourier Transform
The discrete Fourier transform is often used to implement linear time-invariant filters in a computationally efficient manner. This is due to the availability of computationally efficient or fast algorithms for computing the discrete Fourier transform. You will learn about the overlap and add method for computing convolution in this lesson. Overlap and add exploits the efficient computation […]
