Daqarta
Data AcQuisition And Real-Time Analysis
Scope - Spectrum - Spectrogram - Signal Generator
Software for Windows
The following is from the Daqarta Help system:

# Tilt, +/- dB / Octave

Controls: Spectrum Dialog >> Curves >> Tilt, +/-dB / Octave
Macros: LI.TiltdB, LI.Tilt, etc

## Introduction:

This is a straight-line "Curve" that tilts the power spectrum upward or downward as frequency increases, by an adjustable slope given in dB per octave. There are individual controls for each input and output channel, with a button below each control to select it for use.

There are numerous applications for Tilt, as discussed below. Most often, you will want to apply tilts of 3.0103 or 6.0206 dB/Oct, or multiples thereof. These are commonly referred to as 3 and 6 dB per octave. The actual values are based upon the fact that a doubling of power is a change of 10 * log10(2) = 3.0103 dB, and a doubling of voltage is 20 * log10(2) = 6.0206 dB.

So, for example, if a system has a voltage response that falls off proportional to increasing frequency, then the voltage will be halved when the frequency is doubled. This response is termed "falling at 6 dB per octave".

A perfect "pink" noise source has a power response that falls proportional to frequency, so it is said to be "falling at 3 dB per octave".

The maximum Tilt range is +/-24.082 dB/Oct, which is 4 times 6.0206.

Rather than entering values like 3.0103 you can hold down the SHIFT key while clicking the little up/down scroll buttons in the control. The Tilt will change by 3.0103 dB/Oct for each click, so you can just click twice to get a change of 6.0206. Note that the controls only have room for 3 decimal places, but rest assured that you are really getting steps of 3.0103 even though you can only see 3.010.

(If you don't hold down SHIFT, the scroll buttons change the value by exactly 1.00 dB/Oct.)

If you are starting from some arbitrary prior value you can hold down the SHIFT and ALT keys together and the value will be quantized to only multiples of 3.0103.

Note that the difference between 6.0206 and 6 dB/Oct is going to be trivial in most applications. Consider that the entire spectrum consists of 512 frequencies, which amounts to 9 octaves (2^9 = 512). So the worst-case difference, at the highest frequency, will be 9 * 0.0206 = 0.1854 dB. This is likely to be insignificant compared to the noise in most real-world systems.

Tilt does not change your raw data in any way. The Tilt does not get saved with the data when you save to a file, with one exception: It is applied to Text (.TXT) files, which you can use for publication or presentation. For .DQA, .WAV, or .DAT files you must reapply the Tilt when you view the data.

## Pink Noise Correction (+3 dB/Oct):

One application for Tilt is to compensate for using a pink noise stimulus, which can be created with the Daqarta Generator, or via a built-in source on some professional equipment such as recording consoles.

Pink noise has has a spectrum that falls at -3.0103 dB per octave (commonly denoted "3 dB per octave"), which is more representative of real-world signals like music than the flat spectrum of a 'white' noise stimulus. Sound reproduction systems are thus generally designed to handle much more power at lower frequencies; if you used a flat stimulus spectrum you would need to run at very low overall power to avoid burning out the high frequency drivers, but then the low frequencies might be swamped by background sounds.

However, with a pink noise stimulus the 'perfect' system response would be a line that falls at -3 dB per octave, just like the stimulus. It is very difficult to judge how close a line comes to a particular slope, but it is trivial to compare it to the horizontal trace grid to tell if it is flat. However, if you set +3.01 dB Tilt this correction is applied for you: An ideal system would show a flat horizontal response. A real-world system will have dips and/or peaks that deviate from this ideal, and you can easily measure the difference with the cursor readouts.

Note that the Daqarta Pink source spectrum does not fall off at a perfect -3.0103 dB/Oct, but has several ripples of +/-0.85 dB. For critical frequency response measurements, you can create a custom mirror Curve file that will exactly match it and give perfect measurements.

## Step Response Correction:

Another application for Tilt is to allow quick frequency response measurements which might otherwise require a slow frequency sweep or a long noise average. The principle behind this is that the spectrum of an impulse response gives the frequency response of the system.

If you actually try that, you need a very narrow pulse, only one sample wide. You can experiment using the Generator Pulse Wave option. However, there is not a lot of energy in this narrow pulse, and it may be hard for some types of sources to switch on and back off this quickly. A big voltage step, on the other hand, can have a lot of energy and is very easy to create. The derivative of a step function is an impulse function, so it is perfectly "legal" to apply a step to the system and take the derivative of the response to get the impulse response of the system.

The Tilt control simplifies this by making use of the fact that a derivative applies a +6.0206 dB per octave tilt to a spectrum. Here, we simply take the spectrum of the raw waveform, then apply the tilt to the spectrum. If the original spectrum was from a step response, the result will be as though it was from an impulse response. You thus see the frequency response of the whole system on every step.

The Step Response topic covers this method in more detail.

Whether you use an actual impulse, or this Step and Tilt trick, it is important to capture the full response to each event. If the system under test "rings" it must decay to below the noise floor by the end of 1024 samples, or the FFT used to create the spectrum will show the spectrum of the truncated response... not the true spectrum.

Note that sound card inputs and outputs have AC coupling which will pass the ringing, but will greatly reduce or block response frequencies below a few hertz. (But see DC Measurements And Outputs for ways to get true DC input response.)

One tip: Depending upon particulars of your test setup, you may need to adjust the Trigger Delay to eliminate any time lag before the actual response begins. You can usually tell that you need to do this because the raw waveform trace will show a flat portion before the sharp transient of the response. Just add anough trigger delay to eliminate that flat part.

Caution: Step and impulse tests work on the assumption that the system is linear throughout. This is not the case for many real-world systems, such as electromechanical and biological systems, if you push them hard enough. In addition to amplitude limitations like saturation or clipping, which can be troublesome even with conventional swept frequency responses, some systems are susceptible to slew limit problems. This is where the system has some maximum rate of change that it can't exceed; if you drive it with a step or an impulse, it can't change fast enough to respond to the vertical edge, so it does the best it can and instead gives (typically) a constant slope.

This is not the same as the exponential step response you might get from a linear system, and if you drive the system into slew limiting your resultant frequency response will not be the same as a conventional slow frequency sweep response.

This means that you should avoid or use extreme caution with step or impulse methods for basic research that is exploring the response of an unknown system. These methods are best suited to monitoring known systems, such as in production testing of loudspeakers. When you are testing against a known response, even a certain amount of nonlinearity may be perfectly acceptable if you can still detect changes from the standard response.

## Acceleration, Velocity, and Displacement Spectra:

As noted above, taking the derivative of a spectrum is equivalent to applying a +6.0206 dB per octave upward tilt. Conversely, integration is a downward tilt with the same magnitude. You can use these principles to convert between acceleration, velocity, and displacement.

Velocity is the derivative of displacement, and acceleration is the derivative of velocity. If you have data recorded from an accelerometer, you can integrate the acceleration spectrum to a velocity spectrum by applying a -6.0206 dB/Oct Tilt. Using a Tilt of -12.0412 will convert an acceleration spectrum to a displacement spectrum.

## Macro Notes:

LI.TiltdB=3.0103 sets the Left Input Tilt to 3.0103 dB/Oct. Note that there is no macro equivalent to the SHIFT or ALT keyboard shortcuts that can be used when scrolling manually... you have to set the value you want directly, such as with LI.TiltdB=10 * log10(2).

The above Tilt is applied only when the Left Input button below that is on, which you can set with LI.Tilt=1. LI.Tilt=0 switches it off, and LI.Tilt=x toggles between states. Applying any of the Weighting Curve files to Left Input (for example via LI.Curve0=1 will automatically cancel the Tilt state for that channel.

Change the LI. prefix to RI. for Right Input, LO. for Left Output, or RO. for Right Output.

Alternatively, use the Ch. prefix with TiltdB or Tilt to the specify the channel previously given via the Ch Channel Select command.

To find out if a specified channel such as LI is using a Tilt or Curve, assign a variable to LI.SpectCurve?X. The variable will be -1 if the Left Input is not using any Curve or Tilt; otherwise it will hold the Curve number 0-3, or else 4 for Tilt.

To insure that no Tilt (or Curve) is active for a specified channel, use LI.SpectCurve#X= (value ignored) to unselect any Left In (LI.) buttons in the Spectrum Curves dialog. Use other prefixes for other channels, as above, including Ch..

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