Frequency Shifting

This tutorial describes how to perform frequency shifting, causing the frequency of a signal to change.

Frequency Shifting

Frequency shifting is the process of changing the position of a signal within the frequency domain. Equivalently, it can be stated that frequency shifting is the process of changing the center frequency of a signal. Frequency shifted can be implemented many different ways, although this tutorial will focus on the simple method of multiplication by a complex sinusoid.

Multiplying a signal by a complex sinusoid with frequency f Hz will translate or shift the center frequency of the signal by f Hz. For example, to frequency shift a signal by 1 MHz a complex signal must be generated with frequency 1 MHz, and then multiplied against the desired signal in order to frequency shift it.

Build Example Signal

First an example signal needs to be built. A simple signal of filtered noise is created. Drag in the following blocks and connect them:

• Noise Source
• Throttle
• Low Pass Filter
• QT GUI Frequency Sink

The flowgraph is an offline simulation to the choice of sampling rate is somewhat arbitrary, but a sample rate of 10 MHz is chosen to realistic number.

The low-pass filter properties are updated to define the cutoff frequency and transition width:

• Cutoff Freq: samp_rate/8
• Transition Width: samp_rate/16

Running the flowgraph then displays a simulated signal:

The signal has not been shifted yet and therefore has a center frequency of 0 Hz.

Create Complex Sinusoid

A complex sinusoid is added to the flowgraph which will be used later to perform the frequency shifting. Add the following blocks and connect them to the flowgraph:

• Variable
• Signal Source

The flowgraph is an offline simulation to the choice of sampling rate is somewhat arbitrary, but a sample rate of 10 MHz is chosen to be a realistic number.

The variable new_center_frequency is then used for the frequency in the signal source block:

Increase the number of ports on the QT GUI Frequency Sink:

Now run the flowgraph:

You can now see the new complex sinusoid that has been created and displayed in red:

The frequency shifting process will apply the blue signal against the red complex sinusoid, centering it at 1 MHz.

Perform Frequency Shifting

Add the Multiply block into the flowgraph and connect it such that it accepts the outputs from Low Pass Filter and Signal Source:

The multiply block now performs the frequency shifting, moving the center frequency of the signal up to 1 MHz. Running the flowgraph shows the input signal centered at 0 Hz and the frequency shifted version at 1 MHz:

The frequency shifted value can be positive or negative. Update the new_center_frequency variable to be -3 MHz: