# Nyquist frequency, Nyquist rate, digital signal processing time units, n, w, radians/sample. radians/second, Hertz etc.

It seems that DSP becomes confusing when you start, either reading about, or writing about, DSP quantities like filtering and modeling. Here is the scoop on this, to help if you need it.

First, Nyquist frequency and Nyquist rate: A band limited signal may be sampled by another signal (fs) that has a frequency two times the bandwidth ( B). B is called the Nyquist frequency and fs is called the Nyquist rate or simply the sample rate. Nyquist frequency is fs/2 if fs is twice B. These quantities can be normalized to fs = 1 ( normalized to fs) and the Nyquist frequency can be normalized to 0.5. ( Normalized to (fs/2)/fs.). Normalized Nyquist rate = 1. Normalized Nyquist frequency = 0.5. Samples/second. Some CAD tools use the Nyquist frequency as the normalization constant ( MATLAB filter design).

When the non normalized frequency is in terms of w, the angular frequency ( radians/second) and when this is normalized by the sample rate in samples/second the result is in radians/sample. Thus the normalized Nyquist frequency is pi radians/sample, and the normalized Nyquist rate is 2pi radians/sample.

There are also conversions available ( Wikipedia). f(radians/sample)=f(cycles/sec)*(2pi)/fs.

Please visit Signal Processing Group Inc. website for more technical info.

#### FPGA Design and development service

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#### A wideand RF detector ( 40 Mhz to 3 Ghz) -75 dBm to 5 dBm input

A wideband RF detector

#### Linear detector performance

Linear detector performance curves

#### A wideband linear RF detector

Price for one unit: \$25.00. Lead time for delivery 3 days. 30 Day return policy. Pricing for 100 units or more: \$20.00 per unit.  Please contact Signal Processing Group Inc. for details for purchase from Signal Processing Group Inc. Email: spg@signalpro.biz 24/7

#### 2 stage amplifier deta

Please see details at http://www.signalpro.biz/2rf_amplifier_details.htm    Delivery lead time is 3 days. Return within 30 days for a full refund. Price is \$15.00 for one unit and \$10.00 per unit in volumes of 100. For higher volumes than 100 please contact Signal Processing group Inc.

#### Mni LNA performance

Delivery lead time is 3 days. Return within 30 days for a full refund. Price is \$15.00 for one unit and \$12.00 per unit in volumes of 100. For higher volumes than 100 please contact Signal Processing Group Inc. at email: spg@signalpro.biz or call 602-626-0272 for fastest service.

#### A high frequency divider from 500 Mhz to % Ghz+

The input interface.
The frequency divider has a differential analog interface. The following parameters apply:
The minimum frequency that can be input is 500 Mhz and the maximum frequency is 6.0 Ghz.
The RF input level is 5 dBm to – 5 dBm. For lower frequencies make sure that the slew rate is
greater than 560 V/us. The input is biased by two 500 Ohm resistors connected to a 1.6V DC bias.
Therefore AC coupling is used at the input. These are two 100pF capacitors.
The output interface.
The output is single ended. The output driver is capable of sourcing and sinking 24 mA. The
equivalent output impedance is 50 Ohm. To avoid reflections it is recommended that the divider
work into a 50 Ohm load.
General operation.
The inputs are applied to the input SMA I/O. The product will work with both a differential input as
well as a single ended input. However, a differential input works best. The division ratio is applied
to the N1 and N2 control inputs as follows:
N2 N1 Division ratio
0 0 8
0 1 16
1 0 32
1 1 64
The logic levels are:
Logic level Voltage
1 1.4V minimum
0 0.6V maximum
The supply voltage interface.
The operating supply voltage is 3.3V typical. The quiescent (DC) operating supply current is 2 mA.

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#### DC to 3 Ghz RF SPDT switch

RF Switch typical features

Supply voltage = Vcc = 0/+5 Vdc
Operatng temperature = TA = -50° C to 125 Deg C
Operating impedance = 50 Ohm
Input power for 1 dB
compression ( 5.0V system) = 37 dBm ( f = 0.5 to 3 Ghz)
Input third order Intercept = 64 dBm ( 0 to 5.0V system, f = 0.5 to 3 Ghz)
Operating frequency range = DC to 3 Ghz.
Insertion loss DC to 3 Ghz = 0.8 dB
Isolation DC to 3 Ghz = 14 dB minimum
Return loss DC to 3 Ghz = 20 dB
50% contl to 10/90 %
( ON/OFF) = 120 ns

#### A single stage RF amplifier summary specifications

Summary Specifications

Gain,  Operating: 19.5 dB
Operating frequency range: 1.0 – 2700 Mhz
OIP3: (Pout = 19.0 dBm),  -8.5 dBm
P1dB: 4.6 dBm
N.F: 4.2 dB
Supply voltage Operating: 3.3  – 5.5 Volts

Price: single unit \$7.50, 100 units : \$5:50.

Free delivery, shipping lead time 2 days.

30 day return policy, buyer ships.
Supply current Supply = 5.0V,  23.0 mA