Zener noise is variable depending on the device fabrication and parameters, so you can't in general get a fixed noise level from a zener in the same way that you can just order a 5.6V Zener and know that it'll produce that certain breakdown voltage with whatever tolerance is applicable. Of course you can buy characterized and specified purpose built noise diodes which will be guaranteed to produce a certain characteristic of noise under a given set of operating conditions but these are rare or expensive or not necessarily applicable depending on how you want your noise shaped.
The other commenter is correct that you can use a noise source and a variable or selected attenuator to produce a given maximum noise level from a source or some attenuated value from that source, though the source noise density and bandwidth itself might vary depending on age, voltage, current, temperature, load impedance, et. al. so you'll need to measure and select a configuration to produce the appropriate level output for a given source and operating condition.
A common way to adjust the level of a signal would be to use an AGC amplifier such that you apply a variable gain or loss to an input signal such that the power or peak or envelope of the output signal is at some predefined level, and the "automatic" part of the "gain control" will act as a control system to keep the level within your desired setpoint. There are many AGC amplifiers for RF / IF applications that would be applicable -- check Analog Devices, Linear Technology, TI, AVAGO and similar vendors for part options.
Many kinds of resistors have theoretically predictable thermal noise characteristics depending on the measurement bandwidth, resistor temperature, and resistance value, though the noise level is generally much lower than a good noise diode, and often controlled relatively high temperatures are required to generate a lot of noise (relative to other options).
https://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise
You could use a peseudo random digital generator made by a CPLD, MCU, or other logic device implementing a LFSR or other pseudo random sequence generator and feed that output through whatever kind of DAC, filter, and buffer you require to get a fixed level noise output -- the DAC would generate a predictable output level and the filter / buffer would have known spectral shape and gain/loss.
I suggest a properly biased zener diode with appropriate shielding and construction, in an oven if necessary, followed by an AGC amplifier and filter.
If I recall correctly you could probably find some application notes about such a setup from places like LINEAR TECHNOLOGY, AVAGO, the old AGILENT / HP diodes/discretes ANs, BSTJ, probably M/A-COM, maybe FAIRCHILD or MICROCHIP or ON-SEMI / old Motorola. Maybe the old National Semiconductor linear applications too.
If you used a small FPGA plus DDS or Sigma Delta DAC you could probably generate a selectable level / spectrally colored noise (if that matters to you) relatively easily.
Edit -- more information --
http://cds.linear.com/docs/en/application-note/an61fa.pdf
(see pages 24-26, and appendix b of an61)
http://www.linear.com/docs/4262
http://www.maximintegrated.com/app-notes/index.mvp/id/3469
1V isn't just simple noise, something is really inducing it. Here are the steps I would take to solve it:
1) Take a look at the power supply to the DSP and whatever else is communicating and see whether they have any kind of noise on them. It's likely the noise you see is induced on VCC and this might be going to the DSP I/O.
2) if you have any kind of switching regulator, try and use an LDO and see if it makes a difference
3) Attempt to use a good clean lab power supply to the board if you can
4) Isolate other board parts, turn off everything you don't absolutely need. If the issue disappears, slowly bring up each part until you can nail down what it is that is causing it.
5) Take into account any other strange symptoms. Given the large voltage, it's unlikely that the SPI is the only thing affected.
We might be able to help more if you post a schematic and give more details to the parts and whether you have any kind of switching supply
Best Answer
When you stop at a red light in your car and your FM channel, suddenly fades then resumes. This is known after Stephen Rice as Rician Fading loss by the same RF amplitude being inverted from multipath with phase cancelling for some of the wavelengths of all FM RF signals.
In Wifi, it can be demonstrated MP with software tools that convert the WiFi Received Signal Strength Indicator (RSSI) Voltage into dBm instead of 1 to 3 bars. It doesn’t have to be the entire spectrum of ODFM wavelengths that cancel , but enough to distort some of the packet while the rest of the packet could be full,strength giving you no indication at all of a poor signal with full bars. -70dBm is marginal and -80dBm is easily lost with Ricean Fading.
Often all it takes is at this level is a 1 degree orientation or a 1 or 2mm change in position change in the Wifi dongle or laptop and your signal is full speed again.
welcome to Rician Fading loss, but all the best methods of modulation are used to thwart this. The best mobiles and laptops had orthogonal diversity antennae (two) to choose from, in case of this loss of signal.
Although I have used Netstumbler to receive Wifi RSSI levels so I could reach a far away signal by bouncing off backyard trees when I had moved in before service installed at a time when open Wifi was default on Routers.
But the trickiest example of Rician Fading was an expensive Microwave tower link that was installed in summer and failed in winter. Ground Ice cause a surface reflection with the exact wavelength to cancel the received signal. Often it is the reverse with water instead of snow with ground reflections. But if you ever want to see a Garmin GPS get lost in skyscrapers and move your position 2 blocks over due to skyscrapers in Toronto, welcome to multipath Doppler position error.