TAILIEUCHUNG - Nguyên tắc phân tích tín hiệu ngẫu nhiên và thiết kế tiếng ồn thấp P6

Power Spectral Density of Standard Random Processes — Part 2 This chapter continues the discussion of standard random processes commenced in Chapter 5. Specifically, the power spectral density associated with sampling, quadrature amplitude modulation, and a random walk, are discussed. It is shown that a 1/ f power spectral density is consistent with a summation of bounded random walks. SAMPLED SIGNALS Sampling of signals is widespread with the increasing trend towards processing signals digitally. One goal is to establish, from samples of the signal, the Fourier transform of the signal | Principles of Random Signal Analysis and Low Noise Design The Power Spectral Density and Its Applications. Roy M. Howard Copyright 2002 John Wiley Sons Inc. ISBN 0-471-22617-3 6 Power Spectral Density of Standard Random Processes Part 2 INTRODUCTION This chapter continues the discussion of standard random processes commenced in Chapter 5. Specifically the power spectral density associated with sampling quadrature amplitude modulation and a random walk are discussed. It is shown that a 1 f power spectral density is consistent with a summation of bounded random walks. SAMPLED SIGNALS Sampling of signals is widespread with the increasing trend towards processing signals digitally. One goal is to establish from samples of the signal the Fourier transform of the signal. Consider a signal x that is piecewise smooth on 0 ND as illustrated in Figure . One approach for establishing the Fourier transform of such a signal is to use a Riemann sum Spivak 1994 p. 279 to approximate the integral defining the Fourier transform that is Jo - Y Y x pD e-j2npDf - 2 p i x t e-j2nft dt D xND e 2 lj If x is piecewise smooth on 0 T then from Theorem it has bounded variation on this interval. It then follows from Theorem that this 179 180 POWER SPECTRAL DENSITY OF STANDARD RANDOM PROCESSES PART 2 O-------- --------- --------- --------- --------- --------- --------- ----- t D 2D 3D ND Figure Piecewise smooth function on 0 ND . approximation can be made arbitrarily accurate by increasing the number of samples taken. The following theorem establishes an exact relationship between this Riemann sum and the Fourier transform of x. This relationship facilitates evaluation of the power spectral density of a sampled signal. Theorem . Sampling Relationship Consider N 1 samples taken at 0 D . ND sec with a sampling frequency fs 1 D Hz of a piecewise smooth signal x see Figure . If X is the Fourier transform of x and . . . lim X ND f - kfs k M converges for all f e R

• Kĩ thuật Viễn thông
• Tiếng ồn thấp
• thiết kế tiếng ồn
• phân tích tiếng ồn
• tín hiệu ngẫu nhiên
• phân tích tín hiệu
• ô nhiễm tiếng ồn
• ô nhiễm không khí
• âm thanh tần số thấp
• ngưỡn bắt đầu nghe
• ngưỡng chói tai
• cường độ âm thanh
• luận văn
• Thiết kế mạch RF
• mạch RF
• bán dẫn lưỡng cực
• tiếng ồn dao động
• mô hình RF