Time and frequency domain signal conversion method and device

Abstract

The invention discloses a time-frequency domain signal conversion method and a device. The method comprises the following steps: determining the number of terms p+1 of a Taylor expansion of x(i) according to the number N of the inputted time domain signals x(i); determining a first conversion constant mr (wherein r is in the range from 1 to p) and a second conversion constant d according to p anda maximal allowable error; multiplying ar by 2<mr>, wherein ar=(-j2 pi)<r> / (N<r>r!), rounding, and representing the result by binary system; setting the number of the maximal binary digits included in p binary results as t, and setting n(r, i) as the value of the (t-i) binary digit represented by binary (ar*r<mr>( (r is in the range from 1 to p); accumulating x(i) according to yk(i) (shown as above) and S(k, i) being equal to (q|kq is equivalent to imod N, q belongs to (0, 1, 2, ellipsis, N-1)), wherein k, i are in the range from 0 to N-1; calculating mk(r) being equal to sum(yk(i)i<r>), wherein i is in the range from 1 to N-1; calculating mk'(r) being equal to (mk(r) divided by 2<m(r-d)>); and calculating X(k) being equal to the sum of yk(0), mk(0) and the product of sum(sum(-j)<r>(r,i)mk'(r)) and 2<t-i> divided by 2<d>, wherein i is in the range from 0 to t and r is in the range from 1 to p to obtain the frequency domain signals X(k) of x(i). The method can greatly improve the conversion speed between time domain signals and frequency domain signals, thereby improving the hardware implementation efficiency, reducing the hardware implementation complexity, reducing the chip area and power consumption for hardware implementation, and meeting the requirement for real-time signal processing and communication.

Description

technical field [0001] The invention relates to the technical field of signal processing, in particular to a time-frequency domain signal conversion method and device. Background technique [0002] Discrete Fourier Transform (DFT, Discrete Fourier Transfer) is a form of expression of Fourier transform in the digital domain, which describes the relationship between discrete signals in the time domain and frequency domain, so that the processing of digital signals can be easily transformed between the two domains. With the rapid development of electronic technology and integrated circuit technology, digital signal processing has been widely used in the fields of voice processing, image processing, communication and multimedia. [0003] DFT can be expressed by the following formula: [0004] X ( k ) = Σ r = 0 N - ...

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Problems solved by technology

[0015] However, the above-mentioned process of converting time-domain signals into frequency-domain signals still requires floating-point multiplication, and multiplication is a very resource-intensive operation. Not only does it take a long time to calculate, but it also consumes more resources on the hardware.

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