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Author: Albert H. Kaiser
Publisher: GRIN Verlag
ISBN: 3638639142
Category :
Languages : en
Pages : 89
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Book Description
Seminar paper from the year 1997 in the subject Technology, grade: 1 (A), Loughborough University (Department of Aeronautical and Automotive Engineering), language: English, abstract: Conventionally a signal is a physical variable that changes with time and contains information. The signal may be represented in analogue (continuos) or discrete (digital) form. The majority of the physical variables of interest for the engineer are of analogue form. However digital data acquisition equipment favour a digital representation of the analogue signal. The digital representation of a analogue signal will effect the characteristic of the signal. Thus an understanding of the underlying principles involved in signal processing is essential in order to retain the basic information of the original signal. The primary goal to use the Discrete Fourier Transform (DFT) is to approximate the Fourier Transform of a continuous time signal. The DFT is discrete in time and frequency domain and has two important properties: - the DFT is periodic with the sampling frequency - the DFT is symmetric about the Nyquist frequency Due to the limitations of the DFT there are three possible phenomena that could result in errors between computed and desired transform. - Aliasing - Picket Fence Effect - Leakage The DFT of a signal uses only a finite record length of the signal. Thus the input signal for the DFT can be considered as the result of multiplying the signal with a window function. Multiplication in the time domain results in convolution in the frequency domain, which will influence the spectral characteristic of the sampled signal. In the table below rectangular and Hanning window are compared: [...] Table The Fast Fourier Transform (FFT) is a computationally efficient algorithm for evaluating the DFT of a signal. It is imported to appreciate the properties of the FFT if it is to be used effectively for the analysis of signals. In order to avoid aliasing and resulting misi
Author: Albert H. Kaiser
Publisher: GRIN Verlag
ISBN: 3638639142
Category :
Languages : en
Pages : 89
Get Book
Book Description
Seminar paper from the year 1997 in the subject Technology, grade: 1 (A), Loughborough University (Department of Aeronautical and Automotive Engineering), language: English, abstract: Conventionally a signal is a physical variable that changes with time and contains information. The signal may be represented in analogue (continuos) or discrete (digital) form. The majority of the physical variables of interest for the engineer are of analogue form. However digital data acquisition equipment favour a digital representation of the analogue signal. The digital representation of a analogue signal will effect the characteristic of the signal. Thus an understanding of the underlying principles involved in signal processing is essential in order to retain the basic information of the original signal. The primary goal to use the Discrete Fourier Transform (DFT) is to approximate the Fourier Transform of a continuous time signal. The DFT is discrete in time and frequency domain and has two important properties: - the DFT is periodic with the sampling frequency - the DFT is symmetric about the Nyquist frequency Due to the limitations of the DFT there are three possible phenomena that could result in errors between computed and desired transform. - Aliasing - Picket Fence Effect - Leakage The DFT of a signal uses only a finite record length of the signal. Thus the input signal for the DFT can be considered as the result of multiplying the signal with a window function. Multiplication in the time domain results in convolution in the frequency domain, which will influence the spectral characteristic of the sampled signal. In the table below rectangular and Hanning window are compared: [...] Table The Fast Fourier Transform (FFT) is a computationally efficient algorithm for evaluating the DFT of a signal. It is imported to appreciate the properties of the FFT if it is to be used effectively for the analysis of signals. In order to avoid aliasing and resulting misi
Author: Albert H. Kaiser
Publisher: GRIN Verlag
ISBN: 3638136817
Category : Technology & Engineering
Languages : en
Pages : 43
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Book Description
Seminar paper from the year 1997 in the subject Technology, grade: 1 (A), Loughborough University (Department of Aeronautical and Automotive Engineering), language: English, abstract: Conventionally a signal is a physical variable that changes with time and contains information. The signal may be represented in analogue (continuos) or discrete (digital) form. The majority of the physical variables of interest for the engineer are of analogue form. However digital data acquisition equipment favour a digital representation of the analogue signal. The digital representation of a analogue signal will effect the characteristic of the signal. Thus an understanding of the underlying principles involved in signal processing is essential in order to retain the basic information of the original signal. The primary goal to use the Discrete Fourier Transform (DFT) is to approximate the Fourier Transform of a continuous time signal. The DFT is discrete in time and frequency domain and has two important properties: - the DFT is periodic with the sampling frequency - the DFT is symmetric about the Nyquist frequency Due to the limitations of the DFT there are three possible phenomena that could result in errors between computed and desired transform. - Aliasing - Picket Fence Effect - Leakage The DFT of a signal uses only a finite record length of the signal. Thus the input signal for the DFT can be considered as the result of multiplying the signal with a window function. Multiplication in the time domain results in convolution in the frequency domain, which will influence the spectral characteristic of the sampled signal. In the table below rectangular and Hanning window are compared: [...] Table The Fast Fourier Transform (FFT) is a computationally efficient algorithm for evaluating the DFT of a signal. It is imported to appreciate the properties of the FFT if it is to be used effectively for the analysis of signals. In order to avoid aliasing and resulting misinterpretation of measurement data the following steps should be followed: [...]
Author: K.R. Rao
Publisher: Springer Science & Business Media
ISBN: 1402066295
Category : Mathematics
Languages : en
Pages : 437
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Book Description
This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing. As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics. This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.
Author: Allen B. Downey
Publisher: "O'Reilly Media, Inc."
ISBN: 149193851X
Category : Technology & Engineering
Languages : en
Pages : 168
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Book Description
If you understand basic mathematics and know how to program with Python, you’re ready to dive into signal processing. While most resources start with theory to teach this complex subject, this practical book introduces techniques by showing you how they’re applied in the real world. In the first chapter alone, you’ll be able to decompose a sound into its harmonics, modify the harmonics, and generate new sounds. Author Allen Downey explains techniques such as spectral decomposition, filtering, convolution, and the Fast Fourier Transform. This book also provides exercises and code examples to help you understand the material. You’ll explore: Periodic signals and their spectrums Harmonic structure of simple waveforms Chirps and other sounds whose spectrum changes over time Noise signals and natural sources of noise The autocorrelation function for estimating pitch The discrete cosine transform (DCT) for compression The Fast Fourier Transform for spectral analysis Relating operations in time to filters in the frequency domain Linear time-invariant (LTI) system theory Amplitude modulation (AM) used in radio Other books in this series include Think Stats and Think Bayes, also by Allen Downey.
Author: Sonali Bagchi
Publisher: Springer Science & Business Media
ISBN: 1461549256
Category : Technology & Engineering
Languages : en
Pages : 216
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Book Description
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.
Author: E. Oran Brigham
Publisher: Pearson
ISBN:
Category : Mathematics
Languages : en
Pages : 474
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Book Description
The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.
Author: Hari Krishna
Publisher: Routledge
ISBN: 1351454978
Category : Technology & Engineering
Languages : en
Pages : 664
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Book Description
Digital Signal Processing Algorithms describes computational number theory and its applications to deriving fast algorithms for digital signal processing. It demonstrates the importance of computational number theory in the design of digital signal processing algorithms and clearly describes the nature and structure of the algorithms themselves. The book has two primary focuses: first, it establishes the properties of discrete-time sequence indices and their corresponding fast algorithms; and second, it investigates the properties of the discrete-time sequences and the corresponding fast algorithms for processing these sequences. Digital Signal Processing Algorithms examines three of the most common computational tasks that occur in digital signal processing; namely, cyclic convolution, acyclic convolution, and discrete Fourier transformation. The application of number theory to deriving fast and efficient algorithms for these three and related computationally intensive tasks is clearly discussed and illustrated with examples. Its comprehensive coverage of digital signal processing, computer arithmetic, and coding theory makes Digital Signal Processing Algorithms an excellent reference for practicing engineers. The authors' intent to demystify the abstract nature of number theory and the related algebra is evident throughout the text, providing clear and precise coverage of the quickly evolving field of digital signal processing.
Author: C. Sidney Burrus
Publisher: Lulu.com
ISBN: 1300461640
Category : Technology & Engineering
Languages : en
Pages : 256
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Book Description
This book uses an index map, a polynomial decomposition, an operator factorization, and a conversion to a filter to develop a very general and efficient description of fast algorithms to calculate the discrete Fourier transform (DFT). The work of Winograd is outlined, chapters by Selesnick, Pueschel, and Johnson are included, and computer programs are provided.
Author: Eleanor Chu
Publisher: CRC Press
ISBN: 1000687570
Category : Mathematics
Languages : en
Pages : 272
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Book Description
Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transform
Author: E. Oran Brigham
Publisher: Prentice Hall
ISBN:
Category : Mathematics
Languages : en
Pages : 272
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Book Description
The fourier transform; Fourier transform properties; Convolution and correlation; Fourier series and sampled waveforms; The discrete fourier transform; Discrete convolutiion and correlation; Applying the discrete fourier transform.
