MT Modulate AM (SSB)

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Updated2023-02-17
8 minute(s) read

Performs single sideband (SSB) amplitude modulation. This node performs signal processing on data and operates independently of hardware settings. Use this node in both simulated and hardware-equipped applications.

Inputs/Outputs

message signal

Message signal used to modulate the carrier wave.

modulation index

Desired modulation index of the AM modulated waveform parameter. A value of 0.7, for example, corresponds to a modulation index of 70%. A value greater than unity may cause overmodulation and distortion. The node ignores this parameter if you set the suppress carrier? parameter to TRUE.

Default value: 1.0

hilbert filter

The complex-valued Hilbert filter used for sideband cancellation during generation of the AM-SSB baseband complex signal. The node applies this filter to the message signal for generating the baseband complex analytic signal.

Note Changes to the Hilbert filter take effect when the reset? parameter is set to TRUE.

taps

The length (N), in taps, of the Hilbert filter.

design

The underlying design of the Hilbert filter.

Windowed Hilbert Transformer	Generates the length Hilbert filter based on the impulse response.
Equiripple Hilbert transformer	Generates an equiripple Hilbert filter.

Default value: Equiripple Hilbert transformer

peak message amplitude

Peak message amplitude of the message signal parameter. The node uses this value to scale or normalize the input message signal prior to modulation. This value must be positive.

Default value: 1.0

error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Default value: No error

sideband

A value that indicates whether the AM-SSB modulator retains the lower or upper sideband of the message spectrum to generate the AM-SSB baseband complex analytic signal.

Lower sideband	Retains the portion of the message spectrum lying in the negative frequency range and eliminates the positive sideband spectrum.
Upper sideband	Retains the message spectrum spanning the positive frequency range .

Default value: upper sideband

pilot tone

Parameters for specifying pilot tone generation. The pilot tone is added to the Hilbert-filtered complex baseband signal to generate the modulated waveform. The pilot tone provides a coherent phase reference during demodulation for performing carrier phase and carrier frequency offset correction. Set the amplitude parameter to 0 to disable addition of the pilot tone.

Tip Adding a pilot tone is optional when suppress carrier? is set to FALSE. In this case, the presence of the DC component in the AM signal (corresponding to the pure carrier tone) provides a coherent reference for phase and frequency offset correction, therefore the pilot tone is not needed.

frequency

Frequency of the complex exponential tone that is added to the complex baseband signal. Ensure that the absolute value of this tone frequency is less than the Nyquist frequency 1/(2 * dt).

Note When specifying pilot tone parameters, ensure that the pilot tone is added to a portion of the spectrum where the message component of the signal is absent. Conflict between the pilot tone and message signals can cause a residual carrier phase and frequency offset error after demodulation. For example, if you specify a negative pilot tone frequency, specify an upper sideband in the sideband parameter.

amplitude

Amplitude of the complex exponential tone that is added to the complex analytic baseband signal.

suppress carrier?

A Boolean that determines whether to suppress the carrier of the modulated signal.

TRUE	The DC component corresponding to the carrier tone in the amplitude-modulated baseband signal is suppressed.
FALSE	The output amplitude-modulated baseband signal consists of a DC component corresponding to the carrier tone.

Default value: FALSE

reset?

A Boolean that determines whether the node continues AM-SSB modulation using internal states from previous iterations.

TRUE	The node restarts AM-SSB modulation, redesigns the Hilbert filter, and clears internal filter states on each call.
FALSE	The node does not change the Hilbert filter design across multiple calls, and sets the internal filter state to ensure continuous filter operation.

Default value: TRUE

AM modulated waveform

The modulated complex baseband time-domain data for demodulation.

t0

The trigger (start) time of the Y array.

Default value: 0.0

dt

Time interval between data points in the Y array.

Default value: 1.0

Y

The complex-valued signal-only baseband modulated waveform. The real and imaginary parts of this complex data array correspond to the in-phase (I) and quadrature-phase (Q) data, respectively.

error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Adjusting the Carrier Phase

initial phase MT Upconvert Baseband initial phase

Avoiding Distortion

message signal

Prescaling Behavior

This node prescales the message signal parameter by the scalar peak amplitude prior to modulation. The default value of 1.0 for peak message amplitude indicates that no prescaling occurs.

Single Sideband (SSB) Amplitude Modulation

SSB amplitude modulation ensures bandwidth reduction by only retaining either the upper or lower sideband in the message spectrum after the modulation process. The following figure illustrates the series of algorithms applied to the incoming signal m(t). The node applies the AM-DSB algorithms and then applies the Hilbert filter to remove the signal.

When suppress carrier? is set to FALSE, the output amplitude-modulated signal is represented by the following formula:

s_{D S B} (t) = 1 + k \times \frac{m (t)}{\max | m (t) |}

s_{D S B} (t) = 1 + k \times \frac{m (t)}{\max | m (t) |}

s_{S S B (t)} = s_{D S B} (t) \otimes (h_{i} \pm j \times h_{q} (t)) + A_{p i l o t} e^{j ω_{p i l o t}}

s_{S S B (t)} = s_{D S B} (t) \otimes (h_{i} \pm j \times h_{q} (t)) + A_{p i l o t} e^{j ω_{p i l o t}}

where

m(t) represents the message signal data

S _DSB (t) represents the double sideband AM modulated signal (unsuppressed carrier)

S _SSB (t) represents the single sideband AM modulated signal (unsuppressed carrier)

k represents the modulation index

A _pilot represents the amplitude of the pilot tone

ω _pilot represents the frequency of the pilot tone

h _i represents the real component of the Hilbert filter

h _q represents the imaginary component of the Hilbert filter

When suppress carrier? is set to TRUE, the output amplitude-modulated signal is represented by the following formula:

s_{D S B S C} (t) = k \times \frac{m (t)}{\max | m (t) |}

s_{D S B S C} (t) = k \times \frac{m (t)}{\max | m (t) |}

s_{S S B S C} = s_{D S B S C} (t) \otimes (h_{i} \pm j \times h_{q} (t)) + A_{p i l o t} e^{j ω_{p i l o t}}

s_{S S B S C} = s_{D S B S C} (t) \otimes (h_{i} \pm j \times h_{q} (t)) + A_{p i l o t} e^{j ω_{p i l o t}}

where

m(t) represents the message signal data

S _DSBSC (t) represents the double sideband AM modulated signal (unsuppressed carrier)

S _SSBSC (t) represents the single sideband AM modulated signal (unsuppressed carrier)

k represents the modulation index

A _pilot represents the amplitude of the pilot tone

ω _pilot represents the frequency of the pilot tone

h _i represents the real component of the Hilbert filter

h _q represents the imaginary component of the Hilbert filter

In both suppressed and unsuppressed carrier cases, one of two possible Hilbert filter designs is specified using the design element in the Hilbert filter cluster. Select either a Windowed Hilbert transformer or an Equiripple Hilbert transformer.

The Windowed Hilbert transformer generates a length N Hilbert filter with an impulse response h(n) given by the following equation:

ωh (n) = δ (n - \frac{N}{2}) + j \times {\frac{2}{π} \frac{\sin^{2} (\frac{π n}{2})}{\begin{matrix} n \\ 0, n = 0 \end{matrix}}, n \neq 0}

ωh (n) = δ (n - \frac{N}{2}) + j \times {\frac{2}{π} \frac{\sin^{2} (\frac{π n}{2})}{\begin{matrix} n \\ 0, n = 0 \end{matrix}}, n \neq 0}

The Equiripple Hilbert transformer generates a length N Hilbert filter with an impulse response h(n) given by the following equation:

h (n) = g (n) e^{\pm j \times 0.25 \times n}

h (n) = g (n) e^{\pm j \times 0.25 \times n}

where g(n) represents an equiripple lowpass filter with a normalized cutoff frequency of 0.25 Hz.

LabVIEW Modulation Toolkit

Table of Contents

MT Modulate AM (SSB)

Inputs/Outputs

message signal

modulation index

hilbert filter

taps

design

peak message amplitude

error in

sideband

pilot tone

frequency

amplitude

suppress carrier?

reset?

AM modulated waveform

t0

dt

Y

error out

Adjusting the Carrier Phase

Avoiding Distortion

Prescaling Behavior

Single Sideband (SSB) Amplitude Modulation

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