Method and apparatus for interpolating between data samples
First Claim
1. A method of producing interpolated values that contain accurate information about the frequency spectrum of an analog signal which has been band-limited and then sampled, the method comprising the steps of:
- (a) storing data samples of the analog signal; and
,(b) interpolating between said data samples to produce interpolated values, the interpolating comprising the substeps of;
(b1) receiving an unconstrained selection of resample times at which said stored data samples are to be interpolated;
(b2) weighting a set of said stored data samples with a continuous nonrectangular impulse response of a filter having a predetermined frequency response comprising a substantially flat passband and suitably attenuating stopbands, said weighting producing a plurality of convolution values at each of said unconstrained selection of resample times; and
,(b3) summing said plurality of convolution values at each of said unconstrained selection of resample times and producing an interpolated value at each of said unconstrained selection of resample times.
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Abstract
A method and apparatus for interpolating between data samples (VS) that preserves the frequency spectrum of a sampled analog signal (VO) is provided. Data samples (VS) are interpolated to produce interpolated values (VIV) that contain frequency domain information that accurately replicates an original frequency spectrum (24) of the analog signal (VO) is disclosed. A signal processor (10) reads data samples (VS) which occur at sampling times (tS) and resample times (tR) at which the VS values are interpolated. A set of tS times are found near each tR time. A digital FIR filter having a frequency function (H(fT)) and a continuous impulse response function ##EQU1## is embodied in software form within a program that controls the signal processor (10) where T is the width of the filter impulse response. The signal processor (10) convolves an offset continuous impulse response function ##EQU2## with the VS values. A plurality of convolved values (VC) are summed at each tR time to produce an interpolated value (VIV) at each tR time. The frequency response function (H(fT)) of the digital FIR filter reduces aliasing errors introduced by spectral images (25a and 25b) of the original frequency spectrum (24) and reduces amplitude errors caused by the filter'"'"'s pass band ripple (38). The VIV values contain frequency domain information that accurately replicates the original frequency spectrum (24).
52 Citations
15 Claims
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1. A method of producing interpolated values that contain accurate information about the frequency spectrum of an analog signal which has been band-limited and then sampled, the method comprising the steps of:
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(a) storing data samples of the analog signal; and
,(b) interpolating between said data samples to produce interpolated values, the interpolating comprising the substeps of; (b1) receiving an unconstrained selection of resample times at which said stored data samples are to be interpolated; (b2) weighting a set of said stored data samples with a continuous nonrectangular impulse response of a filter having a predetermined frequency response comprising a substantially flat passband and suitably attenuating stopbands, said weighting producing a plurality of convolution values at each of said unconstrained selection of resample times; and
,(b3) summing said plurality of convolution values at each of said unconstrained selection of resample times and producing an interpolated value at each of said unconstrained selection of resample times. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. An apparatus for producing interpolated values that contain accurate information about the frequency spectrum of an analog signal which has been band-limited and then sampled, the apparatus comprising:
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(a) a receiver for receiving data samples of the analog signal; and
,(b) interpolating means coupled to said receiver for receiving said data samples and an unconstrained selection of resample times at which said data samples are to be interpolated, said interpolating means interpolating between said data samples to produce interpolated values at said resample times, wherein said interpolating means includes (b1) a filter producing a continuous nonrectangular impulse response and an associated frequency response; (b2) a data locator coupled to said receiver for receiving said data samples and said resample times and locating a set of said data samples located near each of said resample times; (b3) convolving means, coupled to said data filter and said data locator, for each of said resample times, weighting the set of the data samples with the continuous nonrectangular impulse response of the filter to produce a plurality of convolution values; and (b4) a summer coupled to the convolving means which sums the plurality of convolution values at each of the resample times to produce one of the interpolated values at each of the resample times. - View Dependent Claims (9, 10, 11, 12, 13, 14, 15)
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Specification