Sanjit K. Mitra – författare

The growth in the field of digital signal processing began with the simulation of continuous-time systems in the 1950s, even though the origin of the field can be traced back to 400 years when methods were developed to solve numerically problems such as interpolation and integration. During the last 40 years, there have been phenomenal advances in the theory and application of digital signal processing. In many applications, the representation of a discrete-time signal or a sys­ tem in the frequency domain is of interest. To this end, the discrete-time Fourier transform (DTFT) and the z-transform are often used. In the case of a discrete-time signal of finite length, the most widely used frequency-domain representation is the discrete Fourier transform (DFT) which results in a finite­ length sequence in the frequency domain. The DFT is simply composed of the samples of the DTFT of the sequence at equally spaced frequency points, or equivalently, the samples of its z-transform at equally spaced points on the unit circle. The DFT provides information about the spectral contents of the signal at equally spaced discrete frequency points, and thus, can be used for spectral analysis of signals. Various techniques, commonly known as the fast Fourier transform (FFT) algorithms, have been advanced for the efficient com­ putation of the DFT. An important tool in digital signal processing is the linear convolution of two finite-length signals, which often can be implemented very efficiently using the DFT.

A color time-varying image can be described as a three-dimensional vector (representing the colors in an appropriate color space) defined on a three-dimensional spatiotemporal space. In conventional analog television a one-dimensional signal suitable for transmission over a communication channel is obtained by sampling the scene in the vertical and tem­ poral directions and by frequency-multiplexing the luminance and chrominance informa­ tion. In digital processing and transmission systems, sampling is applied in the horizontal direction, too, on a signal which has been already scanned in the vertical and temporal directions or directly in three dimensions when using some solid-state sensor. As a conse­ quence, in recent years it has been considered quite natural to assess the potential advan­ tages arising from an entire multidimensional approach to the processing of video signals. As a simple but significant example, a composite color video signal, such as the conven­ tional PAL or NTSC signal, possesses a three-dimensional spectrum which, by using suitable three-dimensional filters, permits horizontal sampling at a rate which is less than that re­ quired for correctly sampling the equivalent one-dimensional signal. More recently it has been widely recognized that the improvement of the picture quality in current and advanced television systems requires well-chosen signal processing algorithms which are multidimen­ sional in nature within the demanding constraints of a real-time implementation.

A color time-varying image can be described as a three-dimensional vector (representing the colors in an appropriate color space) defined on a three-dimensional spatiotemporal space. In conventional analog television a one-dimensional signal suitable for transmission over a communication channel is obtained by sampling the scene in the vertical and tem­ poral directions and by frequency-multiplexing the luminance and chrominance informa­ tion. In digital processing and transmission systems, sampling is applied in the horizontal direction, too, on a signal which has been already scanned in the vertical and temporal directions or directly in three dimensions when using some solid-state sensor. As a conse­ quence, in recent years it has been considered quite natural to assess the potential advan­ tages arising from an entire multidimensional approach to the processing of video signals. As a simple but significant example, a composite color video signal, such as the conven­ tional PAL or NTSC signal, possesses a three-dimensional spectrum which, by using suitable three-dimensional filters, permits horizontal sampling at a rate which is less than that re­ quired for correctly sampling the equivalent one-dimensional signal. More recently it has been widely recognized that the improvement of the picture quality in current and advanced television systems requires well-chosen signal processing algorithms which are multidimen­ sional in nature within the demanding constraints of a real-time implementation.

The growth in the field of digital signal processing began with the simulation of continuous-time systems in the 1950s, even though the origin of the field can be traced back to 400 years when methods were developed to solve numerically problems such as interpolation and integration. During the last 40 years, there have been phenomenal advances in the theory and application of digital signal processing. In many applications, the representation of a discrete-time signal or a sys­ tem in the frequency domain is of interest. To this end, the discrete-time Fourier transform (DTFT) and the z-transform are often used. In the case of a discrete-time signal of finite length, the most widely used frequency-domain representation is the discrete Fourier transform (DFT) which results in a finite­ length sequence in the frequency domain. The DFT is simply composed of the samples of the DTFT of the sequence at equally spaced frequency points, or equivalently, the samples of its z-transform at equally spaced points on the unit circle. The DFT provides information about the spectral contents of the signal at equally spaced discrete frequency points, and thus, can be used for spectral analysis of signals. Various techniques, commonly known as the fast Fourier transform (FFT) algorithms, have been advanced for the efficient com­ putation of the DFT. An important tool in digital signal processing is the linear convolution of two finite-length signals, which often can be implemented very efficiently using the DFT.

A color time-varying image can be described as a three-dimensional vector (representing the colors in an appropriate color space) defined on a three-dimensional spatiotemporal space. In conventional analog television a one-dimensional signal suitable for transmission over a communication channel is obtained by sampling the scene in the vertical and tem­ poral directions and by frequency-multiplexing the luminance and chrominance informa­ tion. In digital processing and transmission systems, sampling is applied in the horizontal direction, too, on a signal which has been already scanned in the vertical and temporal directions or directly in three dimensions when using some solid-state sensor. As a conse­ quence, in recent years it has been considered quite natural to assess the potential advan­ tages arising from an entire multidimensional approach to the processing of video signals. As a simple but significant example, a composite color video signal, such as the conven­ tional PAL or NTSC signal, possesses a three-dimensional spectrum which, by using suitable three-dimensional filters, permits horizontal sampling at a rate which is less than that re­ quired for correctly sampling the equivalent one-dimensional signal. More recently it has been widely recognized that the improvement of the picture quality in current and advanced television systems requires well-chosen signal processing algorithms which are multidimen­ sional in nature within the demanding constraints of a real-time implementation.