FFT
=====
| **Block:** FFT (``fft``)
| **Block Author**: Aaron Parsons
| **Block Maintainer**: Andrew Martens
| **Document Author**: Aaron Parsons, Andrew Martens
+--------------------------------------------------------------------------+
| .. raw:: html |
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| .. rubric:: Contents |
| :name: contents |
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| .. raw:: html |
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| |
| - `Summary <#summary>`__ |
| - `Mask Parameters <#mask-parameters>`__ |
| - `Ports <#ports>`__ |
| - `Description <#description>`__ |
+--------------------------------------------------------------------------+
Summary
---------
Computes the Fast Fourier Transform with 2\ :sup:`N` channels for time
samples presented 2\ :sup:`P` at a time in parallel. Uses a biplex FFT
architecture under the hood which has been extended to handled time
samples in parallel. For P = 0, this block accepts two independent,
parallel streams (labelled as pols) and computes the FFT of each
independently (the biplex architecture provides this for free). Data is
output in normal frequency order, meaning that channel 0 (corresponding
to DC) is output first, followed by channel 1, on up to channel
2\ :sup:`N` − 1 (which can be interpreted as channel -1). When
multiple time samples are presented in parallel on the input, multiple
frequency samples are output in parallel.
Mask Parameters
-----------------
+--------------------+--------------------+--------------------+--------------------+
| Parameter | Variable | Description | Recommended Value |
+====================+====================+====================+====================+
| Number | n\_streams | The number of | |
| simultaneous | | input data streams | |
| streams | | to be processed in | |
| | | parallel. Each | |
| | | stream consists of | |
| | | a set of parallel | |
| | | inputs set by | |
| | | another parameter | |
| | | (see Number of | |
| | | Simultaneous | |
| | | Inputs) | |
+--------------------+--------------------+--------------------+--------------------+
| Size of FFT: (2^?) | FFTSize | The number of | |
| | | channels computed | |
| | | in the complex FFT | |
| | | core. The number | |
| | | of channels output | |
| | | for each real | |
| | | stream is half of | |
| | | this. | |
+--------------------+--------------------+--------------------+--------------------+
| Input Bit Width | input\_bit\_width | The number of bits | To make optimal |
| | | in each real and | use of BRAM => 18 |
| | | imaginary sample | For low FFT noise |
| | | as they are | => 25 |
| | | carried through | |
| | | the FFT. Each FFT | |
| | | stage will round | |
| | | numbers back down | |
| | | to this number of | |
| | | bits after | |
| | | performing a | |
| | | butterfly | |
| | | computation if bit | |
| | | growth is not | |
| | | enabled. | |
+--------------------+--------------------+--------------------+--------------------+
| Input binary point | bin\_pt | The position of | |
| | | the binary point | |
| | | in the input data. | |
+--------------------+--------------------+--------------------+--------------------+
| Coefficient Bit | coeff\_bit\_width | The number of bits | 18 |
| Width | | used in the real | |
| | | and imaginary part | |
| | | of the twiddle | |
| | | factors at each | |
| | | stage. | |
+--------------------+--------------------+--------------------+--------------------+
| Number of | n\_inputs | The number of | |
| Simultaneous | | parallel time | |
| Inputs: (2^?) | | samples which are | |
| | | presented to the | |
| | | FFT core each | |
| | | clock. This must | |
| | | be at least | |
| | | 2\ :sup:`2`. The | |
| | | number of output | |
| | | ports is half of | |
| | | this value. | |
+--------------------+--------------------+--------------------+--------------------+
| Unscramble output | unscramble | The FFT inherently | |
| (ie, put channels | | produces data in | |
| in canonical | | an order that | |
| order) | | requires | |
| | | unscrambling | |
| | | before being used | |
| | | by many | |
| | | algorithms. This | |
| | | requires resources | |
| | | and can limit | |
| | | performance and so | |
| | | should be disabled | |
| | | if not necessary. | |
+--------------------+--------------------+--------------------+--------------------+
| Asynchronous | async | Whether valid data | |
| operation | | is input on every | |
| | | clock cycle or is | |
| | | flagged via the en | |
| | | input port. | |
+--------------------+--------------------+--------------------+--------------------+
| Quantization | quantization | Specifies the | NOT Truncate. |
| Behavior | | rounding behavior | |
| | | used at the end of | |
| | | each twiddle and | |
| | | butterfly | |
| | | computation to | |
| | | return to the | |
| | | number of bits | |
| | | specified above. | |
+--------------------+--------------------+--------------------+--------------------+
| Overflow Behavior | overflow | Indicates the | Wrap as Saturate |
| | | behavior of the | will not make |
| | | FFT core when the | overflow |
| | | value of a sample | corruption better |
| | | exceeds what can | behaved. |
| | | be expressed in | |
| | | the specified bit | |
| | | width. | |
+--------------------+--------------------+--------------------+--------------------+
| Add Latency | add\_latency | Latency through | 1 |
| | | adders in the FFT. | |
+--------------------+--------------------+--------------------+--------------------+
| Mult Latency | mult\_latency | Latency through | 2 |
| | | multipliers in the | |
| | | FFT. | |
+--------------------+--------------------+--------------------+--------------------+
| BRAM Latency | bram\_latency | Latency through | 2 For designs |
| | | BRAM in the FFT. | aimed at > 200MHz |
| | | | => 3 |
+--------------------+--------------------+--------------------+--------------------+
| Convert Latency | conv\_latency | Latency through | 1 For designs |
| | | blocks used to | aimed at > 180Mhz |
| | | reduce bit widths | => 2 |
| | | after twiddle and | |
| | | butterfly stages. | |
+--------------------+--------------------+--------------------+--------------------+
| Number bits above | coeffs\_bit\_limit | Determines the | 8 (ensures at |
| which to store | | threshold at which | least 2^8=256 bits |
| stage's | | the twiddle | out of 18432 bits |
| coefficients in | | coefficients in a | of BRAM used) |
| BRAM (2^? bits) | | stage are stored | |
| | | in BRAM. Below | |
| | | this threshold | |
| | | distributed RAM is | |
| | | used. | |
+--------------------+--------------------+--------------------+--------------------+
| Number bits above | delays\_bit\_limit | Determines the | 8 (ensures at |
| which to implement | | threshold at which | least 2^8=256 bits |
| stage's delays in | | data delays in a | out of 18432 bits |
| BRAM (2^? bits) | | stage are stored | of BRAM used) |
| | | in BRAM. Below | |
| | | this threshold | |
| | | distributed RAM is | |
| | | used. | |
+--------------------+--------------------+--------------------+--------------------+
| BRAM sharing in | coeff\_sharing | Real and imaginary | |
| coeff storage | | components of | |
| | | twiddle factors | |
| | | can be generated | |
| | | from the same set | |
| | | of coefficients, | |
| | | reducing BRAM use | |
| | | at the cost of | |
| | | some logic. | |
+--------------------+--------------------+--------------------+--------------------+
| Store a fraction | coeff\_decimation | The full set of | |
| of coeff factors | | twiddle factors | |
| where useful | | can be generated | |
| | | from a smaller | |
| | | set, reducing BRAM | |
| | | use at the cost of | |
| | | the some logic. | |
+--------------------+--------------------+--------------------+--------------------+
| Generate coeffs | coeff\_generation | Generate twiddle | To reduce BRAM |
| with multipliers | | factors in the | usage => on. To |
| where useful | | internal | reduce multiplier |
| | | fft\_direct block | usage => off |
| | | using an | |
| | | oscillator with | |
| | | feedback. | |
+--------------------+--------------------+--------------------+--------------------+
| Number calibration | cal\_bits | When generating | For low BRAM usage |
| locations when | | twiddle factors | => 1. For high |
| generating coeffs | | with an oscillator | quality twiddle |
| (2^?) | | with feedback, | factors => 9. |
| | | reference values | |
| | | are used to | |
| | | calibrate the | |
| | | complex | |
| | | exponential | |
| | | generated. | |
+--------------------+--------------------+--------------------+--------------------+
| Feedback rotation | n\_bits\_rotation | When generating | For low error => |
| vector resolution | | the twiddle | 25. For low BRAM |
| | | factors, the | usage => 18. |
| | | resolution of the | |
| | | vector determines | |
| | | how much error | |
| | | accumulates. | |
+--------------------+--------------------+--------------------+--------------------+
| Maximum fanout | max\_fanout | The maximum fanout | |
| | | the twiddle | |
| | | factors are | |
| | | allowed to | |
| | | experience between | |
| | | where they are | |
| | | generated and when | |
| | | they are | |
| | | multiplied with | |
| | | the data stream. | |
| | | As the | |
| | | coefficients are | |
| | | shared, large | |
| | | fanout can occur | |
| | | which can affect | |
| | | maximum timing | |
| | | achievable. | |
| | | Decreasing the | |
| | | maximum fanout | |
| | | allowed should | |
| | | increase possible | |
| | | performance at the | |
| | | expense of some | |
| | | logic. | |
+--------------------+--------------------+--------------------+--------------------+
| Multiplier | mult\_spec | Array of values | 2 (behavioral HDL) |
| specification | | allowing exact | for each stage |
| (0=core, | | specification of | |
| 1=embedded, | | how multipliers | |
| 2=behavioural) | | are implemented at | |
| (left=1st stage) | | each stage. | |
+--------------------+--------------------+--------------------+--------------------+
| Bit growth instead | bit\_growth | Bit growth at | |
| of shifting | | every stage in the | |
| | | FFT can result in | |
| | | overflows which | |
| | | affect data | |
| | | quality. This can | |
| | | be prevented by | |
| | | dividing the data | |
| | | by two on the | |
| | | output of every | |
| | | stage, or by | |
| | | increasing the | |
| | | number of bits in | |
| | | the data stream by | |
| | | one bit. Shifting | |
| | | decreases the | |
| | | dynamic range and | |
| | | possible data | |
| | | quality whereas | |
| | | bit growth | |
| | | increases the | |
| | | resource | |
| | | requirements. | |
+--------------------+--------------------+--------------------+--------------------+
| Max bits to growth | max\_bits | The maximum number | |
| to | | of bits to | |
| | | increase the data | |
| | | path to when the | |
| | | bit growth option | |
| | | is chosen. | |
| | | Shifting is used | |
| | | for FFT stages | |
| | | after this. | |
+--------------------+--------------------+--------------------+--------------------+
| Hardcode shift | hardcode\_shifts | When shifting to | |
| schedule | | prevent overflow, | |
| | | use a fixed | |
| | | shifting schedule. | |
| | | This uses less | |
| | | logic and | |
| | | increases | |
| | | performance when | |
| | | compared to using | |
| | | a dynamic shift | |
| | | schedule. | |
+--------------------+--------------------+--------------------+--------------------+
| Shift schedule | shift\_schedule | When using a fixed | |
| | | shift schedule, | |
| | | use the shift | |
| | | schedule | |
| | | specified. A '1' | |
| | | at position M in | |
| | | the array | |
| | | indicates a shift | |
| | | for the M'th FFT | |
| | | stage, a '0' | |
| | | indicates no | |
| | | shift. | |
+--------------------+--------------------+--------------------+--------------------+
| DSP48 adders in | dsp48\_adders | The butterfly | on (enabled) to |
| butterfly | | operation at each | reduce logic used. |
| | | stage consists of | |
| | | two adders and two | |
| | | subtracters that | |
| | | can be implemented | |
| | | using DSP48 units | |
| | | instead of logic. | |
+--------------------+--------------------+--------------------+--------------------+
Ports
-------
+----------------+----------------+----------------+----------------+----------------+
| Port | Dir | Data Type | Description | Recommended |
| | | | | Use |
+================+================+================+================+================+
| sync | in | Boolean | sync is used | Ensure the |
| | | | to indicate | sync period |
| | | | the last data | complies with |
| | | | word of a | the memo |
| | | | frame of input | describing |
| | | | data. When the | correct use. |
| | | | block is in | |
| | | | asynchronous | |
| | | | operating mode | |
| | | | an active | |
| | | | signal is | |
| | | | aligned with | |
| | | | en being | |
| | | | active. When | |
| | | | the block is | |
| | | | in synchronous | |
| | | | operating | |
| | | | mode, a an | |
| | | | active pulse | |
| | | | is aligned | |
| | | | with the clock | |
| | | | cycle before | |
| | | | the first | |
| | | | valid data of | |
| | | | a new input | |
| | | | frame. | |
+----------------+----------------+----------------+----------------+----------------+
| shift | in | Unsigned | Sets the | |
| | | | shifting | |
| | | | schedule | |
| | | | through the | |
| | | | FFT to prevent | |
| | | | overflow. Bit | |
| | | | 0 specifies | |
| | | | the behavior | |
| | | | of stage 0, | |
| | | | bit 1 of stage | |
| | | | 1, and so on. | |
| | | | If a stage is | |
| | | | set to shift | |
| | | | (with bit = | |
| | | | 1), then every | |
| | | | sample is | |
| | | | divided by 2 | |
| | | | at the output | |
| | | | of that stage. | |
+----------------+----------------+----------------+----------------+----------------+
| in | | consisting of | time-domain | should not |
| | | one (Input Bit | stream(s) to | exceed 0.5 |
| | | Width) width | be | (divide data |
| | | signals per | channelised. | by 2 pre-FFT) |
| | | input. | | |
+----------------+----------------+----------------+----------------+----------------+
| en | in | Boolean | When | |
| | | | asynchronous | |
| | | | operation is | |
| | | | chosen, this | |
| | | | port indicates | |
| | | | that valid | |
| | | | input data is | |
| | | | available on | |
| | | | all input data | |
| | | | ports. | |
+----------------+----------------+----------------+----------------+----------------+
| sync\_out | out | Boolean | Indicates that | |
| | | | data out will | |
| | | | be valid next | |
| | | | clock cycle. | |
+----------------+----------------+----------------+----------------+----------------+
| out | | | channels. | |
+----------------+----------------+----------------+----------------+----------------+
| of | out | Unsigned, one | Indication of | |
| | | bit per input | internal | |
| | | stream | arithmetic | |
| | | | overflow. Not | |
| | | | time aligned | |
| | | | with data. The | |
| | | | most | |
| | | | significant | |
| | | | bit is the | |
| | | | flag for input | |
| | | | stream 0 etc. | |
+----------------+----------------+----------------+----------------+----------------+
Description
-------------
Computes the Fast Fourier Transform with 2\ :sup:`N` channels for time
samples presented 2\ :sup:`P` at a time in parallel. Uses a biplex FFT
architecture under the hood which has been extended to handled time
samples in parallel. For P = 0, this block accepts two independent,
parallel streams (labelled as pols) and computes the FFT of each
independently (the biplex architecture provides this for free). Data is
output in normal frequency order, meaning that channel 0 (corresponding
to DC) is output first, followed by channel 1, on up to channel
2\ :sup:`N` − 1 (which can be interpreted as channel -1). When
multiple time samples are presented in parallel on the input, multiple
frequency samples are output in parallel.