The present disclosure relates generally to the field of signal processing. More particularly, the present disclosure relates to analysis channelizers with even and odd indexed bin centers.
In the signal processing field, channelizers are known algorithms executed by digital signal processors (DSPs) which select a certain frequency band from an input radiofrequency (RF) signal. The standard M-path analysis channelizer center frequencies coincide with the M sampled data frequencies of the M-point discrete Fourier transform (DFT), the frequencies with integer number of cycles per length of M-samples. These are the M multiples of fs/M, the frequencies that alias to direct current (DC) when their sinusoids are down sampled M-to-1. The spacing between center frequencies is also fs/M as is the output sample rate when maximally decimated.
There is a channelizer variation that has its center frequencies offset by the half channel spacing. These center frequencies are located midway between the DFT frequencies and contain (2M+1)/2 cycles per interval per length of M-samples. In this channelizer, the index 0 is not the center frequency of the baseband channel, but rather, the crossover frequency of the adjacent bins centered at ±0.5 cycles per interval. The filters have the same bandwidth and have the same sample rate of the DFT bin centered channelizer. Changes to the standard channelizer to obtain the offset channelizer require a complex heterodyne of the input series or a complex heterodyne of the filter coefficients.
Let us consider a DFT for an odd number of points, say 15 for example. Such a DFT can be implemented by a Good-Thomas (GT) algorithm or by a conventional mixed radix Cooley-Tukey (CT) algorithm. An advantage of using the GT transform is there are no twiddle factors in the algorithm and the arithmetic is performed with real arithmetic and requires fewer arithmetic operations. As a side note, a 16 point CT fast Fourier transform requires 36 real multiplies while a 15 point GT fast Fourier transform requires 10 real multiplies. Interesting and useful modifications to the channelizer structure can be implemented, which avoids the complex heterodyne when converting between the channelizer options. By avoiding the complex multiplies at the input sample rate, the modified channelizers have a reduced signal processing workload. Accordingly, what would be desirable are analysis channelizers which address the foregoing, and other, needs.
The present disclosure relates to analysis channelizers. In one embodiment, the channelizer includes an M-path filter receiving an input signal; a circular buffer in communication with the M-path filter; and an M-point inverse fast Fourier transform (IFFT) circuit in communication with the circular buffer, such that the channelizer aligns spectra of the input signal with spectral responses an odd length, non-maximally decimated filter bank by alternating sign heterodyne of the input signal. The channelizer applies an equivalency theorem to the non-maximally decimated filter bank formed by an odd length polyphaser filter. Advantageously, the M-path filter does not require on-line signal processing to obtain odd-indexed filter centers. In another embodiment, the channelizer alternates a sign heterodyne of a filter coefficient weight.
The foregoing features of the invention will be apparent from the following Detailed Description of the Invention, taken in connection with the accompanying drawings, in which:
The present disclosure relates to analysis channelizers with even and odd indexed bin centers, as described in detail below in connection with
The standard response to the problem that a signal and a filter do not reside at the same center frequency is to move one of them: the signal to the filter (by the Armstrong heterodyne) or the filter to the signal (using the Equivalency theorem). These two options are shown in
The benefits of selecting an M-path channelizer with M selected to be odd integer were explored. We used the fact that while DC resided on an FFT index, the half sample rate resided midway between a pair of FFT indices. The input heterodyne of DC to the half sample rate placed bin centers offset from DC by half the channel spacing. We still have to access alternate input samples to perform sign reversals. While we have avoided the complex rotation we are still accessing input samples at the high input sample rate. We wonder if we can use the odd length FFT with the embedded offset at the half sample rate but avoid the heterodyne of the signal to the half sample rate. We now examine how the alternating sign input data interacts with the filter coefficients.
It is noted that the channelizer 30 (whether implemented as the first processing circuit 32 or the second processing circuit 34) could be implemented using any suitable processor such as an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field-programmable gate array (ASIC), a microprocessor, or as software executed by a general-purpose processor. It is additionally noted that the channelizer 30 could be implemented in a radiofrequency transceiver, which could include, but is not limited to, a cellular transceiver (e.g., base station or mobile device supporting one or more communications protocols such as 3GPP, 4G, 5G, etc.), a satellite transceiver (e.g., an earth station or a satellite in space), a wireless networking transceiver (e.g., a WiFi base station or WiFi-enabled device), a short-range (e.g., Bluetooth) transceiver, or any other radiofrequency transceiver.
If there is a need for an even length transform, one would lose the half sample rate being located midway between DFT frequency indices. We can still use the spectral location between DFT indices at the quarter sample rate. As an example,
Disclosed herein is an M-channel analysis channelizer with frequency bin centers offset from DC by half their channel spacing. This bin location variation is traditionally referred to as odd indexed bin centers. The reason designs use the odd indexed bin centers is that one can form a symmetric allocation of channels with an even number of bin centers. When we have the even indexed bin centers, the symmetric channel assignment have an odd number of channels with one channel centered at DC which may or may not be occupied. Many OFDM based systems avoid centering a channel at DC due to the DC bin corruption by various DC intrusion sources. These sources include analog mixers self-mixing components, analog-to-digital converter (ADC) truncation quantization of input samples, and 2's complement bias due to truncation arithmetic. The traditional response to aligning the bin centers of an analysis channelizer with the offset bin centers of a multichannel odd indexed bin centered received signal is a complex heterodyne applied to the received signal. Another option embeds the heterodyne in the filter weights of the channelizer. As disclosed herein, a channelizer with an odd number of paths and an odd number center frequencies in its IFFT algorithm had an interesting symmetry anomaly. The IFFT bin centers symmetric about DC include the DC bin but the bin centers symmetric about the half sample rate bracketed the half sample rate. The half sample rate resided midway between IFFT bins, the property we desired in the odd indexed channelizer. By translating DC to the half sample rate of a channelizer with an odd number of paths, we had the odd indexed channelizer without the complex heterodyne of data or filter weights. We then showed that under simple conditions, the sign reversals of the signal samples could be embedded in the polyphase filter weights so no operation was applied to input samples at the high input sample rate.
Having thus described the system and method in detail, it is to be understood that the foregoing description is not intended to limit the spirit or scope thereof. It will be understood that the embodiments of the present disclosure described herein are merely exemplary and that a person skilled in the art can make any variations and modification without departing from the spirit and scope of the disclosure. All such variations and modifications, including those discussed above, are intended to be included within the scope of the disclosure. What is desired to be protected by Letters Patent is set forth in the following claims.
This application claims priority to U.S. Provisional Patent Application Ser. No. 63/129,984 filed on Dec. 23, 2020, the entire contents of which is expressly incorporated by reference herein.
Number | Date | Country | |
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63129984 | Dec 2020 | US |
Number | Date | Country | |
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Parent | 17559840 | Dec 2021 | US |
Child | 18198712 | US |