to navigate

to select

to close

On this page

FX GAIN TM

Time-multiplexed fixed-point gain/multiplier block implemented using Xilinx HLS. Multiplies TM data streams by a configurable fixed-point gain coefficient. Supports signed/unsigned arithmetic with independent bit width configuration for input, gain, and output (integer + fractional parts). Pipeline latency: 6 cycles.

Xilinx

Introduction

This block multiplies each sample of a time-multiplexed (TM) input stream by a fixed-point gain coefficient, producing a scaled output stream.

On every rising edge of CLK, if IN_DV = 1, the component performs:

$$ \mathrm{OUT}(n) = \mathrm{IN}(n) \times \mathrm{GAIN}, $$

where all operands are fixed-point numbers with configurable integer and fractional bit widths. The TM Factor property determines how many parallel samples are processed per clock cycle.

Pin Description

IN Input Variable bit TM

Fixed-point input data, always TM. Width: (IN Integer + IN Fraction) × TM Factor Each TM phase receives its corresponding slice of the input bus.

Default: Must be connected

IN_DV Input 1 bit BIT

Input Data Valid, active high. When high, input data is processed. When low, pipeline is stalled. Default: ‘1’ if not connected.

GAIN Input Variable bit BIT VECTOR

Fixed-point gain coefficient, scalar (not TM). Width: GAIN Integer + GAIN Fraction Applied to all TM phases. Can be connected to a register or constant.

Default: Must be connected

OUT Output 16 bit TM

Fixed-point output data, always TM. Width: (OUT Integer + OUT Fraction) × TM Factor Valid data appear after 6 clock cycles from input.

OUT_DV Output 1 bit BIT

Output Data Valid, active high. Asserted when valid output data is available (after 6 cycle latency).

CLK

Global clock. Every rising edge advances the HLS pipeline for all TM phases.

RESET

Synchronous reset, active high. Clears all pipeline stages and internal state machines.

Properties

Property window

IN Integer InBitsInt

Number of bits of the integer part of the input

Number of integer bits of the input signal ($I_\text{in}$). Range: 0 – 128. Together with IN Fraction, defines the input dynamic range and precision.

Default: 16

Options: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128

IN Fraction InBitsFract

Number of bits of the fractional part of the input

Number of fractional bits of the input signal ($F_\text{in}$). Range: 0 – 128. Higher values provide better precision but increase bit width.

Default: 0

IN Sign InSign

Select if the input is signed or unsigned. Sign uses 1 bit of the integer part

Arithmetic type of the input signal:

UNSIGNED → Non-negative values only, range [0, 2^N - 1]
SIGNED → Two’s complement, range [-2^(N-1), 2^(N-1) - 1]

The sign bit uses 1 bit of the integer part.

Default: UNSIGNED

Options: UNSIGNED SIGNED

OUT Integer OutBitsInt

Number of bits of the integer part of the output

Number of integer bits of the output signal ($I_\text{out}$). Range: 0 – 128. Should be sized to prevent overflow: typically ≥ IN Integer + GAIN Integer.

Default: 16

OUT Fraction OutBitsFract

Number of bits of the fractional part of the output

Number of fractional bits of the output signal ($F_\text{out}$). Range: 0 – 128. For full precision: Set to IN Fraction + GAIN Fraction. Can be reduced to save resources (introduces quantization).

Default: 0

OUT Sign OutSing

Select if the output is signed or unsigned. Sign uses 1 bit of the integer part

Arithmetic type of the output signal:

UNSIGNED → Unsigned result
SIGNED → Signed result (required if input or gain are signed)

Default: UNSIGNED

Options: UNSIGNED SIGNED

GAIN Integer GainBitsInt

Number of bits of the integer part of the gain

Number of integer bits of the gain coefficient ($I_\text{gain}$). Range: 0 – 128. Default: 2 (allows gain up to 4.0 in unsigned mode).

Default: 2

GAIN Fraction GainBitsFract

Number of bits of the fractional part of the gain

Number of fractional bits of the gain coefficient ($F_\text{gain}$). Range: 0 – 128. Default: 14 (provides precision of ~0.0001).

Default: 14

GAIN Sign GainSing

Select if the gain is signed or unsigned. Sign uses 1 bit of the integer part

Arithmetic type of the gain coefficient:

UNSIGNED → Positive-only scaling (amplification)
SIGNED → Allows negative gains (inversion)

Default: UNSIGNED

Options: UNSIGNED SIGNED

Time Mux TimeMultiplexing

Set number of samples for each clock cycle

Number of time-multiplexed phases (parallel samples per clock). Allowed values: 2, 4, 8, 16, 32. Higher values increase throughput proportionally but consume more FPGA resources (one HLS instance per TM factor).

Default: 4

Options: 2 4 8 16 32

Functional description

The component implements fixed-point multiplication using Xilinx HLS (High-Level Synthesis) and replicates the operation N times (where N = TM Factor) to support time-multiplexed data streams with high throughput.

Fixed-point format

Each signal (IN, GAIN, OUT) is configured with:

Integer bits: Number of bits for the integer part
Fractional bits: Number of bits for the fractional part
Sign: SIGNED or UNSIGNED arithmetic

Total bit width = Integer bits + Fractional bits.

Input modes

IN: TM bus of width (IN Integer + IN Fraction) × TM Factor
GAIN: Scalar fixed-point coefficient of width GAIN Integer + GAIN Fraction
OUT: TM bus of width (OUT Integer + OUT Fraction) × TM Factor

The GAIN input is not time-multiplexed and applies to all TM phases.

Data valid handshake

IN_DV (input): Input data valid signal, active high
OUT_DV (output): Output data valid signal, active high (after 6 cycle latency)

Mathematical background

For fixed-point multiplication, given:

Input $x$ with $I_x$ integer bits and $F_x$ fractional bits
Gain $g$ with $I_g$ integer bits and $F_g$ fractional bits

The mathematical product is:

$$ y = x \times g = (x \cdot 2^{-F_x}) \times (g \cdot 2^{-F_g}) = (x \times g) \cdot 2^{-(F_x + F_g)} $$

The output format must accommodate the combined dynamic range. Typical configurations:

Align fractional parts: Set OUT Fraction = IN Fraction + GAIN Fraction
Prevent overflow: Set OUT Integer ≥ IN Integer + GAIN Integer

Timing

The HLS-generated IP has a fixed pipeline latency of 6 clock cycles:

Property	Latency (clock cycles)
FX GAIN TM	6

Total system delay: T_delay = 6 × T_CLK.

In TM mode, all phases operate in parallel with the same latency.

Typical use cases

Signal amplitude scaling in ADC front-ends
Programmable gain stages in nuclear/particle physics detectors
Calibration and offset correction in multi-channel systems
Digital filtering coefficient multiplication

Waveform example

Example with TM Factor = 4, Input = [100, 200, 300, 400], GAIN = 2.0 (fixed-point).

Note: 6 clock cycles of latency from input to output.

Frequency Meter

Measures the frequency of an …

FX OFFSET TM

Time-multiplexed fixed-point …

FX GAIN TM

Introduction link

Pin Description link

Properties link

Functional description link

Fixed-point format link

Input modes link

Data valid handshake link

Mathematical background link

Timing link

Typical use cases link

Waveform example link

Introduction

Pin Description

Properties

Functional description

Fixed-point format

Input modes

Data valid handshake

Mathematical background

Timing

Typical use cases

Waveform example