Looking at your scope display, I think adding hysteresis is a very good idea. It should help, as analogsystemsrf suggested. He also suggested a decoupling capacitor for the \$3.3\:\textrm{V}\$ rail. I think that makes sense, too. Worth doing. That said, I do have a minor problem with precisely how he set things up.
The injector is basically (as I understand it) a coil (with a little inherent resistance to it) that is switched by a Darlington, whose emitter goes through a small current-detection resistor to ground. I gather it isn't uncommon to also have a zener across the collector to ground, with a value somewhere around 36-39 V (or more.) (This doesn't mean you can't see very high spikes, though.)
This means I'd probably want to trigger solidly when the voltage rises above around \$32-35\:\textrm{V}\$ and also solidly the other way when the voltage falls below around \$15-16\:\textrm{V}\$. The way I'd want to achieve this, keeping your thoughts about a \$1\:\textrm{M}\Omega\$ input resistor, is to set the two hysteresis lines at \$34\:\mu\textrm{A}\$ (rising-on) and \$15\:\mu\textrm{A}\$ (falling-off.)
simulate this circuit – Schematic created using CircuitLab
Any small signal NPN BJT with a beta over 140 or so should work fine. 2N3904, PN2222A, etc.
I recommend you try out analogsystemsrf design, first. If that works for you, use it and save yourself a resistor. Either way, don't forget to apply the bypass cap.
The basic idea in the above circuit is pretty easy. Both BJT circuits are "balanced" (same resistance pulling their bases upward, balanced to the degree that the resistor values and BJTs are the same.) Either one of them might power up as controlling the other (a BJT collector is able to turn off the opposing BJT -- but only if the opposing BJT isn't turning it off in return.) Which one it is isn't predictable, without the addition of \$R_1\$ to the circuit. \$R_1\$ imbalances this circuit and ensures that \$Q_1\$ powers up as off, which allows \$Q_2\$ to power up as on.
Now, the node at \$Q_1\$'s base will be around \$670\left[\pm 20\right]\:\textrm{mV}\$ when \$Q_1\$ is on and it will have to be at or well below \$600\:\textrm{mV}\$ when off (more than a factor of 10 change in collector current.) There's not much of a difference between that pair of values, when compared with your "signal" which exceeds \$40\:\textrm{V}\$. So we can easily compute a current supplied by \$R_2\$. It will be about \$\frac{V_Z - 0.5\:\textrm{V}}{R_2}\$, which is about \$12\:\mu\textrm{A}\$ when \$V_Z\approx 12.4\:\textrm{V}\$ and is \$\ge 40\:\mu\textrm{A}\$ when \$V_Z\ge 40\:\textrm{V}\$.
Note that using \$R_3=R_4=150\:\textrm{k}\Omega\$ means that with a \$+3.3\:\textrm{V}\$ power supply rail you will see about \$\frac{3.3\:\textrm{V}-0.5\:\textrm{V}}{R_3+R_5}\approx 18\mu\textrm{A}\$.
If \$Q_1\$ is being held off by \$Q_2\$, then you will have approximately \$R_1\vert\vert R_3\approx 19.2\:\textrm{k}\Omega\$ pulling downward on its base. It will take a current of about \$34-36\:\mu\textrm{A}\$ to drive that to the required to the point where \$Q_1\$ is on. This is near my goal of about \$40\:\mu\textrm{A}\$. Certainly close enough for a circuit like this.
If \$Q_1\$ is instead on, then there is already \$18\:\mu\textrm{A}\$ arriving through \$R_3\$ and \$R_5\$, which adds to any current arriving through \$R_2\$. The voltage will go below \$600\:\textrm{mV}\$ and start the process that will move it rapidly below \$500\:\textrm{mV}\$, when the current through \$R_2\$ falls under about \$12\:\mu\textrm{A}\$ (for a combined \$30\:\mu\textrm{A}\$ through the Thevenin impedance of \$19.2\:\textrm{k}\Omega\$.)
So that's a very simple approach to this. It does not tell you how to come up with the values for \$R_3\$ and \$R_5\$ in the first place. But trial and error would move you rapidly towards the right values, anyway. I use a closed equation for doing this, fed by a variety of BJT parameter statistics. But that's just for robustness. For a simple design, the above details provide enough for considering one's own design.
\$R_5\$ and \$R_6\$ do affect the calculations, of course. But mostly they are just "pull-ups" for your needs. I usually just specify them to the algorithm.
Best Answer
Presence of power at frequencies you're not interested in can easily be filtered out. Presence of power at frequencies you ARE interested in is the problem, as this cannot be filtered out.
There are several main sources of noise. It depends on what context you're talking about, though - things such as interference or cross-talk can be considered noise in the context of, say, the signal-to-noise ratio, but when you build a 'low noise amplifier', this refers to intrinsic sources of noise.
One source of noise that is unavoidable is thermal noise. Any object that is not sitting at absolute zero behaves like a black body and radiates electromagnetic radiation. This is a problem for long range RF communications because the black body radiation from the ground, buildings, etc. will appear in the band of interest and put a 'floor' on the level of signal that you can receive. This noise is more or less flat up to around 80 GHz, so the noise power is simply proportional to the bandwidth and temperature. Thermal noise in electronics is called Johnson noise. Johnson noise is generated by electrons (or other charge carriers) wiggling around due to not being at absolute zero. This can be modelled as a voltage source in series or a current source in parallel with each resistor in a circuit. Johnson noise is proportional to bandwidth, temperature, and resistance.
Shot noise is a very different type of noise that occurs when charges move across a gap (vacuum tube) or through a semiconductor junction (diode, BJT). Since charge carriers are discrete (you can count them), charge must be measured in these quantized units. When a current flows, an integer number of charge carriers will move, arriving at random intervals. For large currents, the fluctuation is so small that it is basically undetectable. However, for very small currents, the current will flow in a series of 'pulses', one for each electron. As a result, shot noise becomes a large problem at low signal levels. Shot noise is white; meaning that it is independent of frequency and the overall noise power is proportional to the bandwidth.
Flicker noise, or 1/f noise, is another, different type of noise. This occurs in electronic devices, in addition to Johnson noise and shot noise. Flicker noise is called 1/f noise because the noise power is proportional to the inverse of the frequency - it is high at low frequencies and low at high frequencies. Generally flicker noise is dependent on the DC level.
Other sources of noise are a bit less common, such as avalanche noise. Avalanche noise is caused by avalanche breakdown. During avalanche breakdown, flowing electrons release more electrons and create an exponentially growing current. Devices such as avalanche photodetectors use this effect to detect small numbers of photons by biasing the device just on the edge of avalanche breakdown so a small number of photons hitting the detector will release enough electrons to trigger the breakdown. Current flow during avalanche breakdown is very noisy. In fact, it is so noisy that avalanche diodes are used as RF noise sources for testing various RF components.
Crosstalk, interference, and intermodulation are also sources of unwanted signals, but these are not technically noise. Crosstalk and interference are unwanted signals coming from external sources. Intermodulation comes from non-linearities and causes adjacent channels in the same medium to be superimposed on top of each other. This is a major problem when trying to transmit a large number of channels in parallel as they mix with each other. Generally this is 2 Fa - Fb. For example, if I transmit two channels with 1 kHz spacing on 1 MHz, then I am transmitting 1.000 MHz an 1.001 MHz. IMD means I will get some power on 2*1.000 - 1.001 = 0.999 MHz and 2*1.001 - 1.000 = 1.002 MHz, which would interfere with adjacent channels on the same spacing.