Understanding Time and Frequency Parameters

User Actions

1. Set frequency span

Determines sample rate:

f = 1.28 * span (for zoom data, i.e. complex time samples)

f = 2.56 * span (for baseband data, i.e. real time samples)

And of course, the sample period is

Dt = 1 / f

Span = 10 MHz Megahertz: A unit of frequency equal to one million hertz or cycles per second.

f = 12.8 MHz (zoom)

f = 25.6 MHz (baseband)

Dt = 78.1 ns (zoom)

Dt = 39.1 ns (baseband)

2. Set number of frequency points (Nf) for spectrum traces

Determines maximum Main Time Record length:

max TimeLen = Nfft * Dt = (Nf - 1) / span

where Nfft is the size of the FFT Fast Fourier Transform: A mathematical operation performed on a time-domain signal to yield the individual spectral components that constitute the signal. See Spectrum. and is a power of 2 (512, 1024, ...)

Nfft = 1.28 * (Nf-1) (for zoom data, i.e. complex time samples)

Nfft = 2.56 * (Nf-1) (for baseband data, i.e. real time samples)

Set Nf = 801.

Nfft = 1024 (zoom)

Nfft = 2048 (baseband)

max TimeLen = 80 us (zoom & baseband)

3. Choose window shape

Determines relationship of TimeLen and ResBw (see next table row).

Each time window has an Equivalent Noise Bandwidth (ENBW), which is the bandwidth of a rectangular filter that passes the same noise power as the filter defined by the time window.

Hanning window selected.

Normalized ENBW = 1.50 Hz-sec

4. Set either desired Resolution Bandwidth or desired TimeLen

TimeLen and ResBw are directly related by:

TimeLen = Normalized ENBW / ResBW

Resolution Bandwidth is a qualitative measure of the minimum separation required between two frequency components to be able to visually separate them and, for the VSA, is defined as the Equivalent Noise Bandwidth of the filter, which is determined by the window type that you select and the length of the window.

Specify ResBW = 100 kHz kiloHertz: A radio frequency measurement (one kilohertz = one thousand cycles per second).

TimeLen = 1.50 Hz-sec / 100 kHz = 15 us

5. Set Time Gate parameters (optional)

Disable gating.

VSA actions

6. VSA determines number of time points to acquire for analysis (Na)

Number of Main Time Record points (Na) is determined by

Na = TimeLen / Dt

The actual number of time points acquired from the hardware will be greater than Na to allow resampling filter settling. You can see the actual points captured from the hardware in the Raw Main Time trace.

Na = 192 (zoom)

Na = 384 (baseband)

7. VSA performs time gating

Gate Time Record length (Ng) is determined by

Ng = Gate Length / Dt

and gate position within the Main Time Record is determined by Gate Delay.

No gating.

8. VSA calculates Spectrum trace data

The VSA performs these steps to compute the frequency Spectrum trace data:

1. Apply selected window to
   • No time gating: Main Time Record (length Na)
   • Time gating: Gate Time Record (length Ng)
2. Zero pad Time Record to FFT length (Nfft)
3. Perform FFT

4. Determine number of frequency points for spectral traces Nspec (not all points shown by default)

   • Zoom data: Nspec = Nfft
   • Baseband data: Nspec = Nfft / 2 + 1 (first half of FFT points; other half is mirror copy)

5. Show center frequency points on Spectrum trace (Nf)

Nspec = 1024 (zoom)

Nspec = 1025 (baseband)

User actions

1. Set frequency span

Determines sample rate:

f = 1.28 * span (for zoom data, i.e. complex time samples)

f = 2.56 * span (for baseband data, i.e. real time samples)

And of course, sample period is

Dt = 1 / f

Span = 25 Mhz

f = 32 MHz (zoom)

f = 64 MHz (baseband)

Dt = 31.25 ns (zoom)

Dt = 15.625 ns (baseband)

2. Choose window shape

Each window has an Equivalent Noise Bandwidth (ENBW), which is the bandwidth of a rectangular filter that passes the same noise power as the filter defined by the time window, multiplied by the length of the time window.

Hanning Window selected.

Normalized ENBW = 1.50 Hz-sec

3. Set length of Time trace

For most demods, the length of the Time trace (TimeLen) is determined by the parameters on the Time tab in the Demod Properties dialog. Usually the parameter is named Measurement Interval.

Some demods have the ability to specify some way of searching for a particular section of the modulated signal. In this case, the length of the Time trace can vary each measurement sweep.

The Time trace shows the pre-demod time data that is analyzed by the demodulator and that is FFT'd and shown in the Spectrum trace. The actual time record captured from the measurement hardware is shown in the Raw Main Time trace and the resampled data that is used to search for the analysis interval is shown in the Search Time trace (some demods do not have this trace).

TimeLen = 50 ms

VSA actions

4. VSA determines ResBW

Resolution Bandwidth is a qualitative measure of the minimum separation required between two frequency components to be able to visually separate them and, for the VSA, is defined as the Equivalent Noise Bandwidth of the filter, which is determined by the window type that you select and the length of the window.

To calculate the ResBW of a window, the normalized ENBW of the window is divided by the length of the Time trace (TimeLen).

TimeLen and ResBw are inversely related by:

ResBW = Normalized ENBW / TimeLen

ResBW = 1.50 Hz-sec / 50 ms = 30 Hz

5. VSA determines number of time points to acquire for analysis (Na)

The Search Time length (Na points) is determined by a parameter (usually) named Result Length or Search Length:

Na = Search Time Length / Dt

The actual number of time points acquired from the hardware will be greater than Na to allow resampling filter settling. You can see the actual points captured from the hardware in the Raw Main Time trace.

Search Length = 35 ms

Na (zoom) = 35 ms / 31.25 ns = 1,120,000 points

Na (baseband) = 35 ms / 15.625 ns = 2,240,000 points

6. VSA searches for analysis start boundary within Search Time record

The VSA searches within the Search Time record for some boundary to set as 0 ms. This can be the beginning of the burst or a frame or subframe boundary, depending on the demodulator.

Analysis boundary found 5.5 ms into Search Time record.

Beginning of Search Time trace set as -5.5 ms.

7. VSA creates the Time record

The VSA creates the pre-demod Time record (shown in the Time trace with number of points Nt) by selecting part of the Search Time record as specified by certain parameters on the Time tab (generally called Measurement Interval and Measurement Offset).

The Time trace data is also resampled to align the time record with the beginning of the analysis boundary (in case the boundary falls between two sample points).

See the documentation for the particular demod you are using for more information. In particular, see the Search Time and Time trace topics and the Demod Properties > Time tab topics.

Time trace length = 10 ms

Nt (zoom) = 10 ms / 31.25 ns = 320,000 points

Nt (baseband) = 10 ms / 15.625 ns = 640,000 points

8. VSA calculates Spectrum trace data

The VSA performs these steps to compute the frequency Spectrum trace data:

1. Apply selected window to the time record data shown in Time trace

2. Perform FFT (length of FFT = Nfft)

   • Zoom (complex) data: Nfft = 2^n where n is the smallest integer such that 2^n > Nt (next power of 2 greater than Nt).

   • Baseband (real) data: Nfft = 2 * (2^n) where n is the smallest integer such that 2^(n-1) > Nt (rounding Nt up to a power of two so that there are twice as many points in the FFT as for zoom data. This is because an FFT of real data produces two mirrored copies of the frequency spectrum).

3. Determine number of frequency points for spectral traces Nspec (not all points shown by default)

   • Zoom data: Nspec = Nfft
   • Baseband data: Nspec = Nfft / 2 + 1 (first half of FFT points; other half is mirror copy)

4. Show center frequency points on Spectrum trace (Nf)

   • Zoom data: Nf = Nfft / 1.28
   • Baseband data: Nf = Nfft / 2.56 + 1

Nfft (zoom) = 2^19

Nfft (baseband) = 2^20

Nspec (zoom) = 2^19

Nspec (baseband) = 2^19 + 1

Nf (zoom) = 409,601

Nf (baseband) = 409,601