- Technical Community
- Technology Discussions
- General Technical Discussion
- Seminars & Technical Webcasts
- Analog
- Boards
- Displays
- IP&E; Interconnects, Passives and Electromechanical
- Lighting
- Memory
- Microcontrollers
- Networking
- Power
- Processors
- Programmable Logic
- Sensing
- Software
- Storage
- Systems
- Wireless
- Avnet Solutions
- Other Avnet Boards
- Visible Things
- Arty
- Display Kits
- FMC - Dual Image Sensor
- FMC - DVI I/O
- FMC - HDMI I/O + VITA Image Sensor
- FMC - ISMNET
- SmartFusion2 KickStart Board
- Nano-ITX / Spartan-6 Development Kit
- Spartan-3A-DSP DaVinci Board
- Spartan 3A Evaluation Kit
- Spartan-6 LX16 Evaluation Kit
- Spartan-6 LX150T Development Kit
- Spartan-6 Industrial Video Kit
- Spartan-6 Industrial Ethernet Kit
- Spartan-6 DSP Development Kit
- Spartan-6 / OMAP-L138 Co-Processing Kit
- Spartan-6 LX9 MicroBoard
- Spartan-6 LX75T PCIe Development Kit
- Spartan-6 FPGA Motor Control Development Kit
- Virtex-6 DSP Development Kit
- Virtex-6 LX130T Evaluation Kit
- Xilinx Kintex-7 FPGA DSP Development Kit with High-Speed Analog

Turn on suggestions

Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.

Showing results for

- Technical Community
- :
- Technology Discussions
- :
- Programmable Logic
- :
- Building Filters using FIR Compiler and Simulink -...

Topic Options

- Subscribe to RSS Feed
- Mark Topic as New
- Mark Topic as Read
- Float this Topic for Current User
- Bookmark
- Subscribe
- Printer Friendly Page

Highlighted
# Building Filters using FIR Compiler and Simulink - Normalized Frequency explained

Options

- Mark as New
- Bookmark
- Subscribe
- Subscribe to RSS Feed
- Permalink
- Email to a Friend
- Report Inappropriate Content

07-15-2010 01:01 PM

When building filters using Simulink and Xilinx FIR Compiler, I often get asked about "Normalized Frequency". I'll try to explain it in terms we can all understand.

In the digital domain, a change in sample rate changes the frequency response of a system. That's just life. For example, a digital filter's effective cutoff frequency, stopband, etc change proportional to the sample rate. It’s handy to normalize by the sample rate, so that it’s easy to analyze the filter’s characteristics when you decide to change the sample rate of your design.

MATLAB/Simulink uses several different methods for expressing period, frequency and sample rates. The Filter Design Assistant Tool (FDA Tool) normalizes frequency to half the sample rate (Nyquist), or Fs/2, and expresses frequency in terms of radians/sample. Here’s how that works out:

f (cycles/sec) 2*f (cycles)

fn = ---- ------------- = --- -------- ; Where** fn** is normalized freq; **Fs** is sample freq;

Fs/2 (samples/sec) Fs (sample) ; and **f** is your periodic signal being sampled.

Notice the units. The seconds cancel out leaving you with units of cycles/sample, which is a common measure in DSP. Thinking back to FDA Tool, it displays radians/sample in Normalized mode. In order to get there, we recall that a sinusoid repeats every 2*pi (radians/cycle). In our normalization we are looking at pi (radians/cycle). Whenever we talk in terms of pi, we're referring to angular frequency (versus linear freq.).

Wn = pi(radians/cycle) * fn(cycles/sample); = pi*fn (radians/sample);

For example, let's say I set my sample rate to Fs=100Msps and design the normalized cutoff frequency of a filter to be 0.2 rad/sample. We can rearrange our original normalized equation to calculate the linear frequency.

fn * Fs 0.2 (radians/sample)*100e6 (Msamples/sec)

f = ------------ = ---------------------------------------- = 10 MHz

2 2

Now if I change my sample rate to Fs=80Msps, I can easily figure out that the same filter will have a cutoff frequency of 8MHz.

The MathWorks has a table of Time and Frequency Terminology that might be helpful.

http://www.mathworks.de/access/helpdesk_r13/help/toolbox/dspblks/ch_sign4.html

This will become second nature after working in MATLAB/Simulink for a little while, but it's always fun to revisit first priciples.