I'm not familiar with the behavior of the particular programs you've named, but the obvious (guessed by ear and confirmed with a spectrogram/waterfall tool) difference between these two clips is the audio bandwidth is different.
The clip from SDR Console has audio occupying about 5 kHz of bandwidth, in a file with a 12 kHz sample rate.
The clip from SDR# ...
If you use SDRSharp with an Airspy Mini, instead of an RTL-SDR, the supported sample rates allow up to 6 MHz bandwidth, due to the use of an ADC with a higher sample rate than the RTL2832 is capable of.
For a wider bandwidth display than 6 MHz, you either need to use different software that can scan or stitch across a frequency range, instead of directly ...
Unfortunately you cannot increase the bandwidth much: the sampling rate in RTL2832U is at maximum 3.2 megasamples / second. In theory (Nyquist theorem) you could get ±1.6 MHz banwidth, but that is already pushing the limits of your hardware. The ± in the bandwidth comes from the fact that you are sampling the I and Q, or signals with a 90° phase shift ...
A lot of the RTL-SDR code is open source on GitHub. This code runs just fine on a Raspberry Pi 3B or 4.
The C code inside rtl_tcp to set the frequency is only a few lines long. From a remote system, after starting the TCP connection, send 5 bytes, 1st command byte 0x01, then 4 bytes containing the desired frequency in little-endian 32-bit integer format. ...
Probably not. Looking at the chips:
NXP TDA18271HDC2 is the RF frontend / "tuner" chip.
Afatech AF9033B is the DVB-T demodulator.
Conexant CX23102 is the analog TV demodulator.
NEC (now Renesas) uPD720114 is a USB hub, which shares the USB port between the AF9033B and the CX23102.
Neither the AF9033B nor the CX23102 seems to have a feature to ...
I checked whether I can listen to FM radios as well right before trying to observe the satellite. This seems to point out that it is not about the setup.
That's not true. Your ability to receive something else is still (like in your last question) not an indication of you being able to receive this.
On the contrary. If the settings, especially the antenna, ...
HackRF One will give you 20MHz bandwidth.
Edit for more detail: If you buy the HackRF One instead of the Noelec SDR dongle, you will have 20MHz instead of 2MHz. Note that the HackRF One costs about $300 which is still 10 times cheaper than a spectrum analyzer but 15 times more expensive than the SDR dongle you currently have.
This would indicate that the decoder software (Dump1090) is responsible for setting the SDR to the appropriate frequency
Yes, this is exactly what happens. You can see the relevant code here:
The function that dump1090 calls, rtlsdr_set_center_freq() and all other functions that start with ...
You're pretty clearly experiencing numerical wraparound: the two numbers produced by the ADC combine to a complex number $z=I+jQ$ with $|z|>1$, and thus, numerically, you suddenly get a switchover.
Reduce the gain by 3 dB. This should give you enough headroom.